The wealthy French champions have brought the likes of Zlatan Ibrahimovic, Edinson Cavani and Javier Pastore to the Parc des Princes in recent years and have also been linked with the Barcelona forward.
Despite overseeing a number of big-name signings since his takeover, Al-Khelaifi believes PSG cannot hope to bring in Messi.
"Is there a chance for Messi to join PSG? No, never. If there were no limits at PSG, then we would sign Messi," he told L'Equipe.
"If Messi doesn't join PSG, then that means that there are limits."
Al-Khelaifi also issued a warning to clubs interested in signing PSG players, highlighting reported links between Manchester City and midfielder Blaise Matuidi.
"Interest from Manchester City in Matuidi? I am not worried because they know that if they touch one of our players, then we will be in opposition to them, and we will go and contact their players too," he added.
"We respect all clubs, but if a club tries to buy one of our players, then it will have to face consequences.
"I don't aim this at Manchester City, as from what I know, they did not contact Matuidi."
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