Agree with some of the other posters in that it's impossible to divine when Mourinho will leave despite his comments, so any conjecture regarding his departure in the near future will be unfounded. That said, depending on the timing of his departure, the candidates of choice would probably range from...
Near future: Has to be Sarri, in my opinion. His body of work at Empoli and Napoli over the last half-decade is incredible. He checks off a lot of boxes in terms of the United job - has a clear vision for how he wants his team to perform, very proactive with a great emphasis on attacking football, individuals like Insigne and Mertens have shown great development under him - so he could facilitate Rashford and Martial's growth, and he knows how to use someone like Pogba in ideal terms because he has experience with Hamšík as the needle midfielder.
Plus, if he's appointed in the next couple of seasons, you'll still be able to get 5-10 years out of him if his tenure proves to be successful. I'd take him over Simeone - reckon we need a more proactive coach in attack because Mourinho will leave a strong defensive foundation in place.
Medium term (~5 years): Sarri would be about to hit 65, so he might not be the ideal candidate. Pochettino, Hasenhüttl and Jardim are probably the standout ones in projected terms when you consider the current landscape. All three qualify to the previous category, too - it's just that I really like the aesthetics of Sarri's teams in terms of their comfort on the ball, pressing, hunters' mentality in attack, and the willingness to throw the proverbial kitchen sink at the opposition to chase a game à la Fergie. Nagelsmann as a dark horse candidate.
Long term (7-8 years): does not compute. Impossible to prognosticate in terms of positive growth apart from maybe Nagelsmann - who'll be in his late 30s and quite seasoned. Some of the ones mentioned previously might be in decline or at other elite clubs, Sarri would be close to 70, a new group of would-be great managers might have emerged from the crop of currently active players (Ibrahimović!!!) or players that have just started out as coaches.