A lot of things have been reported on that matter! I am not sure if anyone has a clear picture of what is going on in the case of a possible Mbappe transfer. But if Mbappe also feels that there is not much to be won with this team except for the title in Ligue 1, he will drift further away from the idea to play any longer for PSG. I think he always wanted to take revenge for the defeat against Real Madrid in the Champions League. Mbappe scored 3 goals against them in the Champions League and yet they struck back and Mbappe had to accept that it wasn't enough. I think he is also sick of that and he knows that next time when they are up against each other it would end with the same result.
The news about Mbappe and his next destination is getting funny to me because there is even the possibility for Mbappe to leave PSG for another team other than Liverpool. In fact, Mbappe wants to leave PSG but the team is just trying to put this palyer under pressure to make him stay there because PSG can't have good performance even with a palyer like Mbappe in their team and they know if they lose Mbappe, they can have even worst performance.
https://www.liverpoolecho.co.uk/sport/football/transfer-news/liverpool-transfer-news-live-robertson-27937125
Apart from performance issues I think the Mbappe saga has already turned into much more than just a player being bought or sold. This transfer has drawn so much attention to the club PSG and its owners that for them it would feel like a loss that goes beyond having one less player. Mbappe is such an important figure for them, he is a French player and I think even president Macron has said a word about his hope for Mbappe to stay in France. Khelaifi doesn't want to lose this tugging war because he knows it would fall back negatively on him as well.