The 35-year-old, who guided Argentina to World Cup glory on Sunday, is in the final year of his contract at Parc des Princes.
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This has led to speculation that he could soon be on his way out of Europe, with MLS side Inter Miami eyeing up a stunning transfer.
Meanwhile, Kylian Mbappe, who scored a hat-trick in the final defeat to Argentina, has also been linked with a move away despite recently signing a new deal.
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But Al-Khelaifi has insisted that he wants Messi and Mbappe, who won the Golden Ball and Golden Boot awards, respectively, to stay.
Speaking to RMC Sport via Fabrizio Romano, he said: "We want to keep both Leo Messi and Mbappe, of course.
"They're the best player and the best goalscorer of the World Cup.
"I won't say more about Messi as we have a plan to discuss after the World Cup."
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In a separate interview with Sport, Al-Khelaifi revealed negotiations will take place with Messi after his World Cup celebrations have come to an end.
He told the Spanish news outlet: "I don't want to say anything about Leo, we have an agreement to talk after the World Cup."
Before adding: "I am sad for France, as the leader of a French club, sad for Kylian, who has played the perfect game.
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"But I'm happy for Leo, he's been the icing on the cake, he deserves it and Kylian has many years to win another World Cup."
Despite announcing Sunday's match would be the last World Cup game of his career, Messi has stated that he will not be retiring from international duty anytime soon.
He told TyC Sports: "Obviously I wanted to cap my career with this and I can't ask for anything more.
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"What will happen after this? I've managed to win the Copa America and the World Cup almost at the end.
"I love football, it's what I do. I enjoy being in the national team and want to continue by experiencing a few more games as a world champion."