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Mbappe has long been tipped to swap Ligue 1 giant PSG for LaLiga powerhouse Madrid, while Premier League outfit Liverpool has also been linked previously.
The 22-year-old star is out of contract at the end of 2021-2022, but PSG has remained defiant over Mbappe's future in the French capital.
Al-Khelaifi reiterated that stance as speculation grows heading into Euro 2020 and the off-season.
"I will be clear," Al-Khelaifi said. "Mbappe is going to stay in Paris.
"We will never sell I'm and he will never leave on a free [transfer]. Mbappe has everything he needs in Paris.
"Where can he go? What club, in terms of ambition, can compete with PSG today?
"All I can say is that things are going well, and I hope we can reach an agreement [on a new contract]. 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 enjoyed another remarkable season in which he scored more goals (21) and landed more shots on target (55) than anyone else in Ligue 1, though PSG were dethroned by Lille.
The France international also converted 60.5 per cent of his big chances – a rate that would help ease Madrid's problems with lack of goals outside of Karim Benzema.