The Ligue 1 giants' supremo insists that no offer has been made to bring the striker to the Parc des Princes and distances his side with a move for Arsene Wenger
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Cash-rich PSG are one of only a handful of clubs who have the financial clout to manufacture a move, but Al-Khelaifi has distanced les Parisiens from any possible deal.
"I think we didn't, honestly, talk to [him]. He's a great player, one of the best strikers in the world," the PSG president told Sky Sports News.
The Ligue 1 leaders' president admits that he is an admirer of the Englishman's talent but insists no official approach has been made for his services.
"I think everybody would like to have him, but if you want to talk about the facts, we didn't approach him."
Al-Khelaifi also insisted that the Ligue 1 leaders were not looking to replace Carlo Ancelotti with Arsene Wenger, who has long been linked with the job at the Parc des Princes.
He added: "Arsene Wenger is a great manager, he's done a great job with Arsenal.
"But he has a contract for another year I believe, as I heard from the media, so I think he's staying at Arsenal.
"I cannot talk on his behalf. I don't know what he will decide but we have Carlo and we are satisfied with Carlo Ancelotti."