I don't think Real Madrid will ever sign Mbappe, considering that he previously turned down Real Madrid's offers and preferred money over a brilliant career with Real Madrid. Mbappe is a genius but also arrogant, we know he is just a new kid in football and he doesn't have to have bad traits if he wants to have a lot of titles.
Everything is possible. we all know, Mbappe's attitude and ego is very high. he is a young player, it's normal that his ego is often a problem. Despite his attitude and ego, all football players know that he is a great and talented young player. for the next one or two seasons, it seems unlikely that Mbappe will play for El Real, besides that his contract is still long with PSG, Florentino has said he is no longer interested in Mbappe.
however, it is possible that in the next few seasons, Mbappe could play for Real Madrid. because after all he is a young talent who still has a good career going forward, especially if he plays for Real Madrid. But I don't think Madrid will sign him any time soon. after all, after all, Madrid still has Vinicius Jr and Rodrygo and maybe several other young players who are being targeted by Madrid in the upcoming January transfer window, one of which is young boy Endrick Felipe.
Maybe some days in the near future Kylian Mbappe will forcefully leave PSG out of frustration because he will never win the Champions League not even to talk of the Ballon d'or at French league. Real Madrid are not even focused on his arrival anymore there's this young Brazilian everyone has been chasing they are currently into the player also. If you take good look at Hazard, he has dropped big form since he left Chelsea, Real Madrid should start planning life without him because he will never get better than this.
They are professional teams and of course it will be easy for them to recover from the pain of having been rejected before, so it is still very possible for Mbappe to leave PSG whether it be Real Madrid or another team at any time. Because now rich teams can buy players they like, regardless of the contracts that are still in their old clubs because rich teams can pay for it.
There are many other teams that are richer than PSG, so it is very possible for other rich teams that exist to be able to pay Mbappe more than what he received at PSG.
The problem of money in this era is no longer a problem for big teams, because if they want to achieve many achievements and the players they recruit have the same target. Then of course they will be able to work together well, and I personally have no doubts about that.
About selfishness or arrogance, I think all players also have this factor. But indeed, other players have different levels of selfishness and arrogance because maybe they are also aware of the abilities they have. But for Mbappe with great potential in him, it is only natural that Mbappe has higher selfishness.