The Barcelona attacker was recently linked with a €250m move to the French champions, but the Ligue 1 leaders have categorically denied that he will ever play for them
A recent report in L'Equipe suggested that PSG were ready to spend €250 million in order to lure the Argentina international away from Barca.
However, Al-Khelaifi has made it clear that the four-time Ballon d'Or winner is out of the French giants' reach.
"Messi is a fantastic player," the PSG president was quoted as saying by L'Equipe.
"I read the other day in your paper that he would join PSG. Well, if you have the money to take him to PSG, make him sign a contract and bring him to Paris...
"Is there any chance that the dream of signing Messi will become reality one day? No, PSG will never sign Messi.
"If we did not have any limits, we would sign Messi. He is not coming here, though, because we do have limits. I am happy with the current squad, the best players are already at PSG."
Messi, 26, has a contract with Barcelona until the summer of 2018.