I also think Mbappe won't be able to move to Madrid this season because it would be huge money for the club. Real Madrid won't pay that when next season they can buy Mbappe at a reasonable price. I think nothing serious will happen if Mbappe doesn't play for Real this season, although they will miss such a striker.
Mbappe contract leaves only one more year with PSG, if Real Madrid can't afford the money PSG is asking for, Real Madrid can get Mbappe for free when his contract expires (if PSG fail to sell him to another club). The problem is that PSG will not let Mbappe go for free next season, PSG will continue to try to get some money before the contract expires.
Real Madrid must be smart in reading the situation they are facing, they are in need of a quality striker since Benzema left. Mbappe is considered to be the most suitable figure to fill the vacant position in the striker area. Waiting until the contract expires is a big mistake in my opinion, PSG will consider offers from other clubs if Real Madrid is too economical in spending its money.