For me, I think PSG management will not want to allow Mbappe to leave PSG as a free agent after they have spent so much money on Mbappe. PSG management might give Mbappe another lucrative deal that will make him remain at PSG. PSG has built its team around Mbappe, and it will affect PSG's performance next season if they allow Mbappe to join Real Madrid before the start of next season. But let's wait and see what will play out between Mbappe and PSG.
Initial the management of PSG actually wanted a renewal of contract with mbappe but then he didn't obliged because he already had his mind made up and it was something he didn't seem like he was going back on so he didn't need any conviction or offer to getting him having a change of mind to staying back at PSG at the end of the season, it's been. On the basis that he gets his career better.
Away from PSG there have been other lucrative deals from other leagues such as the saudi league do mbappe of which he's yet to officially respond to but he has been Linked with the Madrid deal more often since this season, I'm sure he's going to Madrid even if the deal isn't officially announced to have been a done deal but all chances are he's going to Madrid more than he would go to another team this season, Madrid has been his dream team after PSG and this has been a long time dream of which it's most likely going to come true in this new season we are about entering, if only he gets the deal signed already, Madrid is very much ready to welcoming him already.
PSG hasn't been a bad deal for hm all the while he did stayed in PSG but then he's quest for something even higher has led to his decision to leave, PSG would definitely still want him around of which if PSG were able to make it to the champions league finals and probably get to win the trophy This season, chances are. Ery high he would have loved to stay back at PSG and probably help them building the team to be even stronger.