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.