The France international has been linked with a move away from the club following his impressive performances since joining from Monaco three years ago.
“I will be clear, Mbappe is going to stay in Paris,” Al-Khelaifi told L’Equipe newspaper. “We will never sell him and he will never leave on a free (transfer). Mbappe has everything he needs in Paris.
“This is Paris, this is his country. He has a mission, not only to play football, but to promote Ligue 1, his country and his capital.”
Mbappe scored 42 goals for PSG in all competitions in the just concluded season.
He is currently on international duty with France in preparation for the 2020 European Championship.