At the moment, Mbappe is guaranteed two games in the Champions League (in the 1/8 finals), if he changes clubs during the winter transfer window, he will lose the right to play in this season of the Champions League. I'm 99% sure that he won't do this.
I will leave one percent to the fact that somehow miraculously he will end up in Liverpool (and will play in the Europa League, which is better than nothing) since in recent days rumors that Liverpool have entered the fight for Mbappe have intensified again.
But let's assume that Mbappe would leave PSG during the winter transfer window, who would benefit from that? I am not perfectly familiar with the regulations rolled out by the UEFA for players who change clubs in winter and played the Champions League already, but would he be allowed to play in the Europa League?
Anyway, if he changed the clubs, who would be the winners? Liverpool most likely no as they would have to pay a transfer fee while they could get him without paying that fee in summer. Mbappe is not the winner because he would not play the CL anymore, he would (I think) not be allowed to play the Europa League and his signing bonus would decrease significantly. Now he can charge a huge signing bonus in summer because his contract expires. So in summary, Mbappe would lose. PSG would get some transfer fee although it will be far below of what they asked for last summer. But they would lose their biggest hope for the CL games. I don't see a winner when this transaction became real in winter and is not just a rumor.
As far as I remember, the meaning of the restrictions when changing clubs is so that a player who started a tournament in one club cannot play for another team during this tournament (probably to avoid the paradox when a player plays for team A in the group stage, but against team A in the playoffs). Mbappe has not played in the Europa League this season so there are no restrictions on him. By the way, it’s funny, but a paradox could theoretically arise. For example, if a player plays in the Champions League and his team is relegated to the Europa League, and the player himself changes clubs, then in the Europa League playoffs he can play against his former club.
Yes, I also think that these are nothing more than rumors and such a transfer will not take place in the winter.