According to Goal, having originally been confident that a deal could be reached, the La Liga giants would not concede to PSG's demands for a fee of €200 million.
Considering the existing condition, Mbappe will now see out the remainder of his contract at PSG. The contract expires at the end of the season.
Meanwhile, PSG’s sporting director, Leonardo, has drawn up a four-man shortlist of forwards to replace Mbappe should he leave the French club.
Tottenham Hotspur’s Harry Kane is one of the names on the list, with Richarlison, and Mohammed Salah said to be among those eyed.
Kane has already been heavily linked with a move away this summer but the striker has confirmed he is staying at Spurs for this term.