"I will not let go of this 'crazy' player," Al-Khelaifi said.
In an interview with , the PSG president said: "I want players proud to wear our jersey, not players who do the job when it suits them."
He recently said he felt he was at a "turning point" in his career and it was time "to take on more responsibility", and has been linked with moves to Liverpool and Real Madrid.
Mbappe scored 39 goals in 43 appearances in all competitions for PSG last season, having played for them the previous season on loan from Ligue 1 rivals Monaco.
"He wants to be more involved in our project to grow with the team, the club. But I explained to him that the responsibilities, it does not ask," Al-Khelaifi said.
"We must go get them, sometimes even tear them away. We do not wait, we provoke.
"As he is very intelligent, I am sure he understood. Will he still be at PSG next year? I am not 100% sure but 200%."
“Nobody forced him to sign here. Nobody pushed him. He came knowingly to join a project."
Those who do not want, or do not understand, we see each other and we talk to each other…
There are of course contracts to be respected, but the priority now is total membership of our project.”
Neymar's contract in the French capital expires in 2022 but he found himself frequently in hot water last season.
In May, French football authorities banned Neymar for three matches after he in the Coupe de France final. He was also reportedly involved in a with his team-mates after a loss to Montpellier, writes BBC football.
In May, the 27-year-old was stripped of the Brazil captaincy for the Copa America, just eight months after being handed the armband.