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.
What do they expect now? It's too late now because Mbappe's contract ends in June and currently if we look at June there are only 2 days left so they won't be able to get Mbappe to extend his current contract.
Whether they want it or not, whether they like it or not, Mbappe will still leave and this happened because PSG's initial mistake was that they were too confident in Mbappe and made them not realize that his conditions were not beneficial for themselves.
Indeed, there may be several possible situations where Mbappe could make a new contract, but I think it would be a bad decision if it was done because it is good for Mbappe to get out of his situation at PSG and he will make a new contract at PSG, which is a really good condition. It's really ridiculous because he is only oriented towards money and luxury.