The Argentina superstar is out of contract at the end of the season and it has been reported during the tournament in Qatar that he had already agreed to terms to move to MLS, where he would join Inter Miami.
Those links have since been downplayed, however, with Messi not set to make a decision on his future until after the World Cup, where Argentina are preparing for a quarter-final showdown against the Netherlands.
Al-Khelaifi is optimistic his two-year spell at Parc des Princes will be extended as, when suggested by Sky Sports that Messi wants to stay in the French capital for longer, he said: "Definitely. He's very happy, you can see that with the national team.
"If a player's not happy you will see their performance is not good for the national team. He performed fantastic this season for us, he's scored a lot of goals and assists for the national team and for the club.
"So, what we agreed together – that after the World Cup, sit down together. But both sides – our side of the club and him – are very happy, so we will talk after the World Cup."
Another player who could be a topic of discussion for PSG after the conclusion of the action in Qatar is England forward Marcus Rashford, who has scored three goals for Gareth Southgate's side in the tournament.
Rashford's contract at Old Trafford is due to expire at the end of the season, though Manchester United have an option to extend for a further year, and Al-Khelaifi confirmed the French champions would look to revive their interest in such a scenario.
"He's another player that is really amazing. And for free? To have Rashford for free, every club would run after him, definitely," he added.
"We're not hiding it, we spoke before and [there was] interest. But the moment was not a good moment for both sides. Maybe, at the end of the season, why not?
"Today if he's a free agent of course we can talk to him directly, but we are not going to talk to him now. Let him focus on the World Cup. Then in January, hopefully, if we're interested we will talk to him."