PSG came into the second leg with a two-goal advantage but were made to work at a raucous Anfield until Dembele scored in the 72nd minute with a wonderful left-footed finish. In added time, the Ballon d’Or winner added a second.

Buoyed by the crowd, Liverpool huffed and puffed in their quest to pull off another memorable European comeback, but Arne Slot’s side failed to score against the holders of the Champions League and, for the second season in a row, they have been knocked out by PSG.

After their feeble display in Paris last week, where they lost 2-0, Liverpool were much better against the French side at Anfield and asked questions, but ultimately it wasn’t enough.

Slot opted to give Alexander Isak his first start since December and left Mohamed Salah on the bench again, but Salah was introduced on the half-hour mark after Hugo Ekitike was forced off with what looked like a worrying injury.

It was the visitors who threatened more in the first half, with Giorgi Mamardashvili making saves to deny Khvicha Kvaratskhelia and Dembele.

Dembele wasted a glorious opportunity when he blazed over with only the keeper to beat. At the other end, Marquinhos made a stunning challenge to deny Liverpool a goal.

Slot made a double substitution at the break, taking off Isak for Cody Gakpo and Jeremie Frimpong for Joe Gomez, and Liverpool started the second half on the front foot but failed to make it count.

In the 65th minute, they were awarded a penalty when Alexis Mac Allister fell down after a challenge by Willian Pacho, but after the video assistant referee (VAR) intervened, the referee Maurizio Mariani overturned the decision.

Seven minutes later, Kvaratskhelia found Dembele, who beat Mamardashvili with pace and power from 20 yards out to put the tie to bed.

And as Anfield emptied out, Dembele tapped in from close range after he was teed up by Bradley Barcola.

Defeat for Liverpool means they will end the season without silverware and it remains to be seen whether they will qualify for Champions League football next season.

The Georgia international, who was linked with Liverpool and Chelsea, asked to leave Serie A leaders Napoli last week after failing to agree a contract extension.

While no details of the transfer fee have been disclosed, reports say French champions PSG have paid 70m euros (£59m) plus add-ons for Kvaratskhelia.

“It’s a dream to be here,” said the 23-year-old winger. I’ve heard so many positive things about PSG.

“I feel immense pride in joining this great club and I’m really looking forward to wearing my new colours.”

Kvaratskhelia – who was part of the Georgia side that reached the last 16 at Euro 2024 – was dubbed ‘Kvaradona’ by supporters during Napoli’s title-winning campaign, after the club’s iconic player Diego Maradona.

He joined Napoli in 2022 for £9m from Georgian club Dinamo Batumi and has claimed a combined 54 goals and assists in 107 appearances.

Kvaratskhelia is PSG’s first signing of the January transfer window and becomes the first Georgian player in the club’s history.

“Khvicha is one of the most exciting players in world football – a fantastic talent, but also a player who has courage and fights for the team above all else,” the club said.

PSG are seven points clear of Marseille at the top of Ligue 1 and visit Lens on Saturday, before hosting Manchester City in the Champions League on Wednesday.

PSG believe they have been left with no alternative other than to respond to Textor’s interview this week with Brazilian publication Globo.

In it, Textor, who through his Eagle Football Holdings group is a majority shareholder in Lyon and the biggest shareholder in Premier League club Crystal Palace, said he was competing against “a country, not an owner” and that PSG were a “model of unbridled spending, without restrictions”.

PSG have been majority-owned since 2011 by Qatar Sports Investments, which has links with the Qatar Investment Authority – the country’s sovereign wealth fund.

In a letter signed by PSG’s general secretary Victoriano Melero, seen by BBC Sport, the club has called Textor’s comments “false, incendiary, undignified and nonsensical”.

They add: “We would like to respond to a few of your most unwarranted smears that are particularly false, hypocritical, and disrespectful not only to PSG but the wider French football family.

“You falsely state PSG has ‘a model of unbridled spending without restrictions’ while ignoring the fact your own club has had significant issues with Uefa and DNCG restrictions under your management.”

French football’s financial watchdog, the DNCG, announced in July last year it would monitor Lyon’s transfers and wage bill for the 2023-24 season after ruling the Ligue 1 club did not provide sufficient financial guarantees.

The measures were lifted in December after the DNCG approved Lyon’s new budget.

In the letter, PSG also highlighted that American Textor criticised the Premier League’s spending rules in February.

They added: “You mention you are competing ‘against a country’ with PSG, ignorant of the fact that a significant portion of our club today is owned by US investor Arctos – which we thought you might be aware of, coming from the US.

“Less than 20% of PSG’s commercial revenue comes from Qatar companies, while PSG has signed 50 new partners in the last six years and only one of these was a Qatari brand.”

PSG end the letter by stating if Textor continues his “defamatory and damaging statements” they “will be forced to add to your growing number of lawsuits in Brazil with additional action in France”.

Textor is the largest shareholder of Brazilian top-flight club Botafogo.

A legal case has been brought against him in Brazil by parties he accused of being involved in corruption and match-fixing, comments which were subsequently dismissed by the domestic football authorities, but which he refused to back down from in his Globo interview.

The deal includes a £1.7m option to buy the 18-year-old winger.

Noha Lemina’s season-long loan at Serie B club Sampdoria was cut short after he only made one appearance over the first half of the season.

“Noha’s an exciting, quick and direct winger,” said Wolves sporting director Matt Hobbs.

“When Mario first joined, his brother had been flagged up by our scouting team.

“Mario’s a driven individual, so doesn’t want any favours, but he has real belief in him and thinks he’s a Premier League player in the making – and Noha will back himself.

“There’s no pressure from anyone here. It’s a chance to look at an exciting young talent.”

The 25-year-old France captain’s deal with the Ligue 1 champions runs out in the summer and he has been heavily linked with a move to Real Madrid.

Mbappe told PSG in June that he would not be taking up an option for a further 12 months in his contract.

“First of all, I’m very, very, very motivated for this year. It’s very important,” said Mbappe.

Speaking after scoring for PSG as they beat Toulouse 2-0 to claim the French Champions Trophy, he added: “As I said, we’ve got titles to go after and we’ve already won one, so that’s already done. After that, no, I haven’t made up my mind yet.

“But in any case, with the agreement I made with the chairman [Nasser Al-Khelaifi] this summer, it doesn’t matter what I decide.

“We managed to protect all parties and preserve the club’s serenity for the challenges ahead, which remains the most important thing. So we’ll say it’s secondary.”

Mbappe joined PSG in 2017, initially on loan from Monaco before a 180m euro (£165.7m) move.

He was set to leave on a free transfer at the end of the 2021-22 season but ultimately signed a two-year contract extension, with the option of a further year.

However, after Mbappe told PSG he would not agree to the additional 12 months of the deal, he was not selected for their pre-season tour to Japan in the summer.

He subsequently refused to meet with representatives of Saudi Pro League side Al-Hilal, who made a world record £259m offer for him.

The striker later returned to first-team training following what PSG said were “very constructive and positive” talks.

Mbappe turned down a move to Real Madrid when he agreed to his current deal with PSG in May 2022 but may not leave a decision on his plans as late this time around.

He added: “I think it was the end of May in 2022 because I didn’t know until May.

“If I know what I want to do, why drag it out? It just doesn’t make sense.”

Meanwhile, Barcelona boss Xavi has said that players like Mbappe are out of reach for the Catalan club because of their financial position.

“I have to deal with the players I have because right now we are not able to think about those kinds of signings,” said Xavi.

“Unfortunately, we are not in a privileged situation economically to do that. I am left with the players I have, and with those players, we have to win.”

PSG’s star forward tried to carry on after an early challenge with Leonardo Balerdi but went off before half-time.

Mbappe could be a doubt when the French champions play Newcastle away in the Champions League on 4 October.

PSG cruised past Marseille after goals by Achraf Hakimi, Randal Kolo Muani and two from Goncalo Ramos.

It lifted them into third spot in Ligue 1, two points behind early-season leaders Brest.

Luis Enrique’s side had lost their previous Ligue 1 game 3-2 at home to Nice on 15 September but they never looked back once Morocco full-back Hakimi scored straight from a free-kick.

Hakimi then provided the cross for Muani to score his first goal since signing from Eintracht Frankfurt for £64.2m plus £12.2m in add-ons earlier this month.

Substitute Ramos sealed the points with the third and fourth goals after replacing the injured Mbappe.

Marseille, whose manager Marcelino resigned last week, should have equalised at 1-0 down but Vitinha headed against the bar.

Their first Ligue 1 defeat of the season leaves them seventh in the table, two points behind PSG.

The 22-year-old scored a hat-trick for Portugal at last year’s World Cup in Qatar and has attracted interest from numerous top European clubs.

He netted 27 goals in 47 appearances for Benfica in the 2022-23 campaign.

Ramos’ arrival comes amid reports in L’Equipe Neymar has told PSG president Nasser Al-Khelaifi he wants to leave.

Meanwhile, the summer-long contract stand-off continues with the club’s all-time leading goalscorer Kylian Mbappe, who is refusing to sign a year’s extension to his contract which ends next summer and wants to join Real Madrid.

The French forward is not currently training with the first team as they prepare for the start of the Ligue 1 season on Saturday.

Ramos is the Ligue 1 club’s ninth major signing of the window following an extensive recruitment drive.

PSG have an option to buy the forward at the end of his loan, similar to the deal that saw Mbappe arrive at the club from Monaco in 2017.

PSG have already signed goalkeeper Arnau Tenas, defenders Milan Skriniar and Lucas Hernandez, midfielders Marco Asensio, Manuel Ugarte, Lee Kang-in and Xavi Simons plus forward Hugo Ekitike.

BBC Sport understands Al-Khelaifi was contacted by the Glazer family a month ago as United’s owners tried to get Qatari banker Sheikh Jassim bin Hamad Al Thani to raise his offer.

The conversation with Al-Khelaifi has led to suggestions of a wider Qatari involvement in Sheikh Jassim’s bid.

Sheikh Jassim has repeatedly said his offer was made in a personal capacity.

Speaking in Istanbul before the Champions League final after a meeting of the influential European Clubs’ Association (ECA) he chairs, Al-Khelaifi said he has done nothing unusual and his involvement is solely with PSG.

“Paris St-Germain is my club, in my heart, and I have nothing to do with Manchester United,” he said.

“It makes me laugh. I am Qatari, right? If people ask me my opinion, I will answer them for sure – and that’s what they do.

“I am talking about anyone, not just Manchester United. I will give them the experience that I have. That’s it.”

Last week, Sheikh Jassim lodged his fifth bid for United, which remains on the table despite suggestions he would not engage with the process beyond last Friday.

He wants to buy 100% of United, while rival bidder Sir Jim Ratcliffe and his Ineos Group are willing to secure a majority stake, which would allow the Glazer family to retain representation in some capacity.

Al Khelaifi is the chairman of beIN Sport, a state-owned broadcaster based in Doha as well as the boss of Qatari Sports Investments.

He demonstrated his willingness to offer advice by revealing last month he spoke to a wealthy group who wanted information around potential investment in two English clubs.

“I’m not going to mention them but one was small, the other big,” he said. “I don’t know who the guy was. But I told him my opinion.”

Al-Khelaifi, who denies he met the Raine Group who are handling the United sale process, says he welcomes new investment into the game, from Qatar and elsewhere.

“I want the best for European competitions,” he said.

“If it’s within the regulation, why not? Not only Qatari, everyone.”

Juventus welcome in ECA after Super League ‘mistake’

Al-Khelaifi also addressed the latest development around the remaining three members of the European Super League and Juventus’ demand for talks with Real Madrid and Barcelona, which they hope will lead to them quitting the project.

The Serie A giants have been mired in financial controversy in recent months as a result of accounting methods that eventually led to a 10-point deduction, which cost them a place in the Champions League.

Juventus had previously remained loyal to the Super League project as they wait for a ruling from the European Courts’ of Justice around whether European football’s governing body Uefa is entitled to hold a monopoly position.

However, Juventus have now stepped away from that position and Al-Khelaifi believes it is the right thing to do.

“It is a smart decision for them to leave,” he said. “There is no future there. They are wasting time, energy and money.

“It makes sense to go back to the family. Everyone makes mistakes. But the smart people realise their mistakes and correct them. We welcome anyone back if they realise their mistakes. That is what they should do.”