Al-Khelaifi was speaking about Kylian Mbappe at a news conference to introduce Luis Enrique as PSG’s new manager following the sacking of Christophe Galtier.
France striker Mbappe, 24, has told PSG that he will not extend his contract with them beyond 2024.
“Our position is very clear,” said Al-Khelaifi.
“If Kylian Mbappe wants to stay – we want him to stay – he needs to sign a new contract.
“We cannot let the best player in the world right now leave for free. That is impossible.”
Kylian Mbappe has the option of a further year when his deal expires after next season but has said that while he plans to stay with the French champions for the 2023-24 campaign, he does not intend to activate the contract extension.
If that is the case, he would be able to leave for free next summer.
“This is a French club and, as he has said, he is not planning to leave for free,” added Al-Khelaifi.
“If somebody has changed his mind, it is not our fault.”
Kylian Mbappe, who joined PSG in 2017 initially on loan from Monaco before a 180m euros (£165.7m) transfer, has scored 212 goals in 260 games for the club.
He finished as Ligue 1’s top scorer in each of the past five seasons and has won five league titles in his six seasons at PSG.
Al-Khelaifi spoke to introduce Luis Enrique at the start of the news conference before making his comments about Mbappe after the Spaniard had spoken to the media.
Former Spain and Barcelona manager Luis Enrique has signed a two-year contract with PSG following the departure of Galtier, who was sacked despite winning the Ligue 1 title in his one season in charge.
It is his first role since he stepped down as Spain manager in December after defeat by Morocco on penalties in the last 16 of the World Cup.
His last job in club management was at Barcelona, where he won nine trophies in three seasons between 2014 and 2017, including the Champions League, La Liga and Copa del Rey Treble in his first campaign in charge.
He went on to replace Fernando Hierro as Spain manager in 2018 and led his country to the final of the Nations League and the semi-finals of the European Championship in 2021.
The former Real Madrid and Barcelona midfielder takes over a PSG squad in transition.
As well as uncertainty about Kylian Mbappe’s future, there is a question mark over the future of Brazil forward Neymar following Argentina captain Lionel Messi’s departure to Inter Miami.
The club’s Qatari owners are intent on trying to build a team rather than continuing the policy of signing high-profile players, which has so far failed to deliver the Champions League success they crave.
Early signs had been promising under Galtier after he replaced Mauricio Pochettino last summer.
PSG started last season strongly with a 22-game unbeaten streak, but lost nine times in all competitions after the resumption following the World Cup.
A 2-1 loss to Marseille in the last 16 of the French Cup in February was followed by defeat against Bayern Munich at the same stage of the Champions League.
And PSG’s league form also waned as they limped to the Ligue 1 title, finishing just one point above runners-up Lens.
Galtier also came under increasing pressure off the pitch after being accused in April of making racist remarks during his time in charge at previous club Nice – allegations that he has denied – and will go on trial in December as a result of an investigation.
PSG said: “The entire Paris St-Germain team would like to thank Christophe Galtier, as well as his assistants Thierry Oleksiak and Joao Sacramento, for their professionalism and commitment throughout the season.”