However, Al-Khelaifi appears to be happy with the job Ancelotti, 53, is doing.
Asked about Ancelotti's future, he told Le Parisien: "If he wants to stay, he will still be here. He has done an excellent job. This has sometimes been difficult because he is under pressure, as in all professions, but he is doing well.
"Carlo is one of the best coaches in the world, if not the best.
"I think he will continue, but at the end of the season we will assess everything. We will also assess my performance. This is normal, it happens at every club."
PSG take on struggling Nancy in Ligue 1 later this afternoon.