I'm not sure they would let him go on a free transfer. Not everyone lives in fantasyland and refuses to accept reality like Levy and Spurs. That said, if he goes to either United or Real Madrid, I don't think either will have enough FFP room to get both Mbappe and Kane. And Kane will probably want to stay in the Premier League in order to break the scoring record.
I think Mbappe does eventually end up at Real Madrid, though, one way or another. Would he go to United for a year? His salary alone is insane. It's hard to find a firm number, depending on the source, but it's in the neighborhood of a million euros per week (or more). So I don't see it for United. But, if Qatar does buy United, maybe it happens (it probably doesn't even then). I would guess Real Madrid is more able to afford his salary than United (Sancho, Martial, Maguire, Fred and others outside the starting XI have pretty big contracts).