I don't think Mane will play for United for several reasons. He has problems with Liverpool staff since he is underpaid comparing to his colleagues but I don't think that he will play against his team and make his fans angry. I think he prefers to play in other league. Bayern would be the best pick for him.
Of course, he won't move to Man United. What he can get in Man United? Seems nothing, it is hard to expect the same achievements as in Liverpool. Man United also has complicated problems in their squad, Mane must think it isn't the right place to continue his career. Bayern should be a better destination for him, he can expect the same goals as in Liverpool. Or he may consider other top clubs that have the same capability as Liverpool, for example Real Madrid, Chelsea, PSG, or Barcelona.