I don't really think Tuchel would suit United. The problem is that he would follow Mounrinho and his current squad is like the antithesis of Tuchel's understanding of football. He prefers midfielders like Weigl and Gündogan who are less vertical players as well as fast, agile and technically profound strikers/forwards. He has the latter with Rashford and Martial but your biggest transfers over the last years, like Lukaku and Pogba, simply don't fit his approach I think. I could hardly imagine them in a Guardiola team and after all, Pep is Tuchel's big role model and when he goes to an international top club, he will most likely want to introduce a similar concept. This would mean that you guys need to restructure your squad again and especially your supposed key players would have to be replaced. Can't see that happening, really.
I think he would fit in brillantly at PSG and Arsenal. However, since he is a difficult character who hates if his superiors intervene with his work, I can see him falling out with the PSG owner/board. Especially if he is only appointed as a placeholder this would mean he has a weak position and I doubt that he would accept that - especially after his experiences in Dortmund. This could also have been a secret reason of why he rejected Bayern since Hoeneß is a difficult character, too, who allegedly wasn't very fond of him in the beginning. Arsenal is an easier environment, I guess. After all, Wenger hadn't had much pressure from his superiors at all. Tuchel also finds some of his old players (Mkhitaryan, Aubameyang) as well as others who brillantly suit his style (Ozil, Wilshere, Bellerin, Kolasinac). He would still need another CM and a CB, if you ask me, but this could be possible. I think he will go to Arsenal, honestly. Just seems the better fit.