Signing Mbappe is a big project for Real Madrid of course, because it is clear that if Mbappe plays for Real Madrid then Real Madrid will have a very good dominance. Because after all, basically Real Madrid are very used to forming star squads and of course, if Mbappe plays at Real Madrid it is not difficult for Real Madrid to get consistent and stable performance. But yes, if next season Real Madrid still can't sign Mbappe, then Real Madrid chance to destroy Manchester City dominance will still be difficult.
Its not easy for signing Mbappe in this summer transfer window, Saudi Pro League teams Al - Hilal reported open proposal bid offer 300 million euro and will give fantastic salary until 173 million euro each years. Real Madrid have fighting with Saudi teams if want sign Mbappe because Madrid won't pay more than 200 euro for fees transfer.
Have Mbappe or not in Real Madrid squad next season I don't difficult for destroying Manchester City dominance in UEFA Champion League, Madrid still have many star players from Vinicus Junior, Jude Bellingham and Arda Guler who are on the young age. I don't think Madrid want pay much fees transfer for signing Mbappe and prefer waiting until that player become free agent next season if not reach deal for extending contract with PSG.