Per BBC Sport's Simon Stone, Mourinho gave an update on the Chile international on Friday:
"So I think Alexis has what I used to call an aggressive muscular injury," he added, per Sky Sports.
Sanchez was left out of United's squad for Tuesday's 1-0 win over Young Boys in the UEFA Champions League, and he has started just one Premier League match since September 22.
The 29-year-old has struggled to justify playing a more significant role, as he has scored just once in his 12 appearances this season. By contrast, Anthony Martial has netted seven times from the left wing.
After news of his injury broke on Thursday, Bleacher Report's Nick Akerman questioned whether Sanchez would feature for the club again:
James Robson of the Evening Standard reported the forward is open to leaving Old Trafford in January but that his exit could be hampered by his injury.
The transfer window could be finished by the time he returns to fitness, and he will have little chance to catch the eye of any suitors while he's on the sidelines. He will therefore likely be stuck at United until at least the summer.
Though he wasn't starting many games for the Red Devils or contributing a great deal when he was on the pitch, his injury is poorly timed ahead of the busy festive period.
With Sanchez out, they can ill afford any more injuries in the coming weeks, as they will need to make full use of their squad to keep players fresh.