Personally, I doubt Man United to sign Mbappe. Man United may have the money to sign him, but Mbappe should prioritize Real Madrid over Man United. Real Madrid is his dream team and Real Madrid offers a bigger chance to win any top trophies. Specifically, Real Madrid is a perfect team for Mbappe if he dreams to win UCL trophy. So, he should assume to have a better career in Real Madrid. Well, because of these reasons, I'm very doubtful if Man United can change Mbappe's mind. Since the chance is likely very small, I think Man United is better to look for another striker.
In addition, Real Madrid constantly monitors Mbappe's situation in PSG. If Mbappe has the intention to leave PSG, Real Madrid must be the first team to know it. So, Real Madrid is likely leading the competition to sign Mbappe.
With the Glazers it seemed impossible, but with the Qatari owners it was no problem for them to bring Mbappe to Old Trafford. now, the problem is with Mbappe, is he ready to leave if in the end PSG puts him on the sale list. then, is Madrid willing to bring him to the Santiago Bernabeu. very interesting isn't it, because Madrid is only waiting for one season if they want Mabppe to join Los Blancos.
To be honest, I don't really know if the final decision rests with Mbappe. or, PSG has full rights to release him in the next season's transfer window. because I also read from several sources that Mbappe has the right not to be with a club that is interested in signing him. but if Madrid are interested in signing him, they could mediate with a fairly commensurate offer. at least, PSG will not lose too much instead of releasing him as a free agent. so is Madrid, who are in need of his services. isn't this a win win solution. if I'm wrong, please correct me because I don't really know about player contract issues.
Last what I heard was that Mbappé wants to leave PSG. And PSG is also interested in selling him right now. Because PSG knows very well that if they wait they might have to let Mbappé go for free. That is going to be a big loss for the club.
I know the owner of PSG is a very rich man. So probably he can take that loss. But honestly, no one wants to lose 200 million for nothing. Well, at least 150 million. And it is almost certain that if they wait and try to get a contract extension they will lose Mbappé for free. They will probably try, though. The only thing they have been trying, and also being successful with that, which is trying to keep Mbappé in the squad by offering a huge amount of money.