If Mourinho is happy in Roma he can stay, but I'm sure there will be a lot of teams that want to see him at the end of this season. The first ones that come to my mind are PSG, Chelsea. I think both of these teams are thinking of changing coaches. One of the biggest candidates for these teams would be Mourinho. Of course, Arab teams that have been making incredible money lately may also want to bring Mourinho. They are currently trying to make the Saudi league the focus of football in the world.
Chelsea has already secured the service of Mauricio Pochettino. The Argentine has signed a two-year contract. It seems after the outburst during and after Roma's loss to Sevilla in the Europa finals, PSG seems to have removed Mourinho from their radar. They have narrowed the target to Nagelsmann. But the news from most sports outlets is that Nagelsmann is the leading candidate with Thierry Henry as a potential assistant.
It is disappointing that Roma failed to qualify for the Champions League because I perceive that was Mourinho's target. The loss motivated him to think of moving to another club. Roma fans see him as a hero and he is well respected there. Saudi Arabian league will offer more money but it will affect his coaching career because the league is not competitive and low rated. Mourinho has to choose between remaining in Roma for at least a season to see if he can win more trophies and promote his coaching career. Or to move to the SPL, make money, and harm his coaching career.