The Parisians slipped to a shock defeat to Rennes in a dramatic penalty shootout, marking the first time in five years that the Ligue 1 heavyweights have failed to win the cup.
After the game, Neymar reportedly questioned the attitudes of some of the young players in PSGs squad, a comment which Mbappe is said to have taken exception too.
Spanish publication Sport report that as one of the youngest in the team at just 20 years of age, Mbappe felt the criticism was directed towards him - prompting manager Tuchel to admit to the press that both players could end up leaving, and he wouldnt have much of a say in the matter.
The German boss said in a recent press conference: "As a coach, I do want them to continue, but this is football, we are not naive.
"Many clubs want to transfer many players and the market is crazy, but if you ask me, the coach, yes, I want them here next season. But if they are not, we will find solutions."
Finding replacements for the pair if they were to leave would not be easy, even for a club with the financial resources of Les Parisians - with the duo scoring 110 goals between them since arriving at the Parc des Princes.
Both Neymar and Mbappe joined the French champions in the summer of 2017 and the club have won Ligue 1 in both seasons the duo have been at the club.
However, the pair were signed in an attempt from the owners to become more successful in Europe and it has not worked out thus far, with PSG being knocked out in the Champions League round of 16 in the last two campaigns.