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.
Roma will be very happy if Mourinho stays with them but to convince Mourinho, they must give him bigger budget for transfer. $7M is what they spent in the last summer transfer and Mourinho was not happy with it.
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.
You can strike out those clubs. Chelsea already appointed Pochettino as their new coach. PSG sacked Galtier and in their conversation to sign with Nagelsman. If PSG actually sign with Nageslman, Mourinho will not have many options to choose, if he does not want to move to Saudi Arabia. A biggest club he can join is Real Madrid as their future with Carlo Ancelotti is unknown and Perez always opens his arms to welcome Mourinho back to Bernabeu.
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.
I believe Mourinho still wants to enjoy matches in Europe than in Saudi Arabia. He can join that league in future but not now and he want to win one more Champions League or one more Europa League in Europe.