Mbappe's contract with the Ligue 1 champions runs out at the end of June and he is free to sign an agreement to join a new club for next season.
"I'm not going to hide that I want Kylian to stay," Al-Khelaifi told broadcaster RMC.
"The best player in the world is Kylian and the best club for him is Paris."
PSG have yet to win a maiden Champions League title despite spending billions of euros on transfer fees since the arrival of their Qatari owners in 2011.
Mbappe has been heavily linked with a possible move to 14-time European champions Real Madrid.
"He has the best training centre in the world, the best coach in the world (Luis Enrique)," said Al-Khelaifi.
"Every year he's sure of playing in the Champions League, we're in the last 16 at least, quarter-finals, even semi-finals or final, we're there with the big clubs."
A source involved in Mbappe's contract negotiations told AFP last week that the France forward had waived bonuses totalling "several tens of millions" of euros in a bid to ease a move away from PSG.
Mbappe signed a contract extension in 2022 which secured him a salary of €72 million (£61 million) per year, a signing bonus of €150 million (£129 million) and a loyalty bonus which rose from €70 million (£60 million) in year one to €90 million (£77.6 million) in year three, according to Le Parisien.
But Al-Khelaifi insisted whether Mbappe stays or not "is not a question of money".
"We have a lot of very important matches, I ask for you to leave Kylian alone, leave him alone."
Mbappe has scored 24 goals in all competitions for Ligue 1 leaders PSG this season.
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