Al-Khelaifi also dismissed speculation that PSG want to replace head coach Mauricio Pochettino with Zinedine Zidane.
Speaking after Lionel Messi became the first player from the club to win Ballon d'Or honours – largely attributed to him winning the Copa America with Argentina – Al-Khelaifi made his position known about the burning issues affecting PSG.
There have been deep worries that Mbappe will walk away on a free transfer at the end of the season, when his current deal expires. Real Madrid wanted him in the last transfer window and are expected to move again. Unless Mbappe commits to a new deal, he would be free to talk to the likes of Madrid from January.
But Al-Khelaifi can see a future in which Mbappe continues to terrorise defences in a PSG shirt, just as he is currently doing in tandem with former Barcelona captain Messi.
The PSG president addressed that within the context of Messi's award success, saying: "For the club, it is the first, I hope it is not the last. I hope that other players will win it, starting with Kylian. I'm sure he wants to win it."
Speaking to L'Equipe, Al-Khelaifi said of the 22-year-old striker's future: "You know what I think, Kylian is a great player, a great man. Kylian knows what he wants to do, us too."
On the potential for new contract talks, the PSG president said, according to RMC Sport: "We hope."
It remains to be seen whether either Mbappe or Pochettino stay in Paris beyond the end of this season.
There have been persistent rumours that PSG would consider swapping Pochettino for former Real Madrid boss Zidane, but Al-Khelaifi threw his support behind the Argentine coach currently at the helm.
"Pochettino is our coach and he is happy to be with us, we are happy to work with him," Al-Khelaifi said.
"He is doing a good job. Everyone needs time. I see all the rumours, we have to stop talking about this, it's not true.
"We're truly happy with the coach. We haven't had any contact with Zidane. He's a great coach, but we also have a very good one."