After his rejection to the real madrid and it seems like that real madrid didn't even care anymore with him. Real was looking for alternative solution. This is a question that can only be answered by real madrid.
When Real Madrid needed Mbappe, he didn't accept the offer. Even though his deal was practically done, he flatly rejected Real Madrid. For the Madrid supporters, it was a great disappointment. Given what has transpired in the past, I don't think he will be taken into consideration; instead, I believe he might play for Liverpool. We don't know what will happen to him by January because he wants to leave, and I believe the club will let him go without holding him back. Every team will want to have Mbappe in their squad because he is a superb player; Liverpool would be at advantage having him in their squad.
I don't really understand the news trending that Mbappe is not happy in PSG, I haven't read any interview granted Mbappe where he said so and also Psg coach has said that Mbappe hasn't discussed anything of that kind with him. I wonder where the news is coming from.
Real Madrid might not be able to secure Mbappe because of the saga between Psg and Real Madrid which all started from Eufa Super league issues.
Liverpool is one of the last clubs to sign Mbappe, they cannot pay him and they cannot maintain him, if not they would have kept Mbappe.