Arsenal have already offered Ozil, in excellent form over the past few weeks, £275,000-a-week to re-sign and have not given up on persuading him to stay but are struggling to reach an agreement.
Mourinho worked with him for three years at Real Madrid when he described him as the best No10 in the world.
“Lazy, arrogant, overrated!” — These Manchester United fans don’t want Arsenal’s Ozil
It would also surely give him satisfaction if he can sign one of bitter rival Arsene Wenger’s best players, on a free.
Barcelona are also keen on Ozil, 29, but there is a growing belief that United could be his destination and their players are beginning to gossip among themselves that they think he will join next summer.
Ozil filmed hugging Manchester United coaches after their win over his Arsenal side
The Germany stalwart, 29, also knows he will be able to command a bigger deal as a free agent in the summer than if he was to be sold in the looming January window.
Wenger has previously admitted he could be tempted to sell Ozil or striker Alexis Sanchez next month but United are unlikely to move for him then.
They would rather wait until he is a free agent.