I'm not sure Mbappe will go to Madrid. despite the news of a contract extension which he did not. there were rumors that he would not choose Madrid. this season Mbappe will still be at PSG in my opinion.
I bet that Mbappe will not stay in PSG because he is facing with pressure to succeed in Champions League and win big individual awards like Ballon d'Or. He feels many times that he won't get it in Paris with PSG. The quick success of Haaland after moving from Dortmund to Manchester City gives Mbappe more reasons to consider leaving PSG.
PSG already experienced some uncertain weeks in the last summer when they had to convince Mbappe signing a new contract. I am sure PSG will not be ready to face with a same similar situation and they know that next times, they will have less chance to convince Mbappe. So if they can get more than $100M from his transfer this summer, they will not waste it.
Moreover, it is also rumored that Madrid will soon complete the transfer of Joselu. he is a striker who is also quite prolific. Madrid chose him and I think it's also a good buy because Real Madrid is looking for a striker to fill in the departure of Benzema.
Joselu just scored a winning goal for Spain against Italy but I should be honest that I did not know about Joselu before that goal. Is he a star player? He is not and I think Real Madrid only sign him to replace Marco Asensio. Joselu is not an alternative solution of Real Madrid for Mbappe.