The France international recently left PSG shocked and disappointed when he informed them that he had no intention of taking up the 12-month extension option in his contract.
As a result, Mbappe will be free to leave the club for nothing at the end of the 2023-24 season, although Al-Khelaifi has already stated that such a scenario will not be allowed to happen.
Despite his stance, Mbappe has affirmed that he plans to continue at PSG for the upcoming campaign and will only make a final decision on his future when he is down to the final few weeks of his contract.
In contrast, PSG are desperate to get rid of the attacker if he refuses to commit his future to the club, and Al-Khelaifi was initially expected to hold showdown talks with the 24-year-old at Campus PSG on Tuesday.
However, Sky Sports News reports that the pair did not speak face-to-face, but Al-Khelaifi has still issued Mbappe with a contract ultimatum, and the France international has until the end of the month to extend his contract or be sold in August.
Rather than engage in a personal conversation with Mbappe, Al-Khelaifi instead addressed the whole group and also took a moment to welcome their six new signings in Milan Skriniar, Marco Asensio, Manuel Ugarte, Lucas Hernandez, Kang-in Lee and Cher Ndour.
During a 15-minute speech, Al-Khelaifi warned all players that no one - not even the president - is bigger than the club, and players that do not want to play for the badge can walk out of the door.
The 49-year-old also affirmed that PSG have "no excuse" for not succeeding this season, as Enrique aims to end the Ligue 1 champions' spate of failures in the Champions League.
While PSG will do their utmost to offload Mbappe if he does not have a change of heart, the ex-Monaco man could be short of offers this summer, as only a handful of clubs could meet PSG's €200m (£173.5m) asking price.
Despite previously snubbing Real Madrid to stay with PSG, a move to the Bernabeu is still seen as the most likely outcome to the saga, especially with Karim Benzema departing for Al-Ittihad this summer.
However, with Arda Guler, Joselu and Jude Bellingham all arriving in the Spanish capital during the current window, Real will likely wait until 2024 before attempting to sign Mbappe on a free transfer.
Manchester United has also been mooted as a potential destination for Mbappe, but only if Sheikh Jassim bin Hamad Al Thani wins the race to purchase the club from the Glazer family.
The 24-year-old is also alleged to prefer a move to Arsenal if he does end up in the Premier League, but the Gunners will not break their wage structure to accommodate Mbappe.
Amid the ceaseless speculation over his future, Mbappe hit a staggering 41 goals in 43 games last season and overtook Edinson Cavani as PSG's all-time leading goalscorer.