Have internal problem with PSG during he won't extends his contract will over on June 2023, left few months later he will be free agent and I don't think PSG happy with this situation depend Mbappe not accept offer from Saudi Pro League who give more excited salary and they want agree release fee transfer above 300 million euro. Mbappe have dreaming winning UEFA Champion League but looks impossible if stay with PSG depend have any teams get bigger chance become the champion.
that the reason Mbappe said several times that he wanted to leave PSG and that has been happening since the transfer at that time and created pressing problems for Mbappe to have to stay at PSG for 1 season until the deadline as you said. Its only natural that he wants to get the experience of having a title at UCL because he has very reliable talent so if he can not get the experience of having title at UCL it will be a waste and if the Arab team wants to give Mbappe a bigger salary, still he will reject it before he gets the target he has to achieve, he will not leave the european team and if you look at the rumors currently spreading, Mbappe is close to team from La Liga and it seems very certain that Mbappe will come to Real Madrid.