In fact, Real Madrid didn't do anything about Kylian Mbappe in this summer, and they were just waiting to see Mbappe get out of his team and they hire him for free without spending money on this player because they knew PSG will put a high amount of money for releasing this player.
I think if Real Madrid really wanted to hire Mbappe for this season, they had to start negotiations with PSG and make this player to join the team like that.
What Mbappe is going through with PSG deemed not professional by many teams and maybe Real is not willing to spend that much money on a player that may end up doing all kinds of moves to get the highest amount of money he could from their team as well. What if he just asks for a transfer fee amount of money as a signing bonus when he is free? That doesn't make sense, if your team pays 100-150 million to him just for signing, and then 50 to 70 million yearly as well, would you feel fine about it?
I mean sure if you pay him 50-70 million alone then I could understand, he is a great striker, and that money could be considered fair, but the 100-150 million fee just to get him? You wouldn't want to also pay to PSG as well. Next summer, when he is free, we will see how much he will want.