Henrikh Mkhitaryan will miss Manchester United's trip to Crystal Palace on Wednesday but is unlikely to be sidelined for a lengthy spell.
The Armenian's afternoon was cut short following a late Danny Rose challenge during United's 1-0 victory over Tottenham on Sunday.
Mkhitaryan scored the winner before being stretchered off in front of a concerned Old Trafford crowd, but Mourinho expects to have the 27-year-old back before the New Year.
"The injury doesn't look like a big one," the United manager said.
"It doesn't look like one needing surgery or months of recovery.
"It depends always on the player - anatomy, physiology, mentality - but hopefully it is not a big thing."
Mourinho later told the club's in-house channel MUTV: "Hopefully we have him for Boxing Day."
Meanwhile, the United boss was relieved after his side secured their first Premier League win at Old Trafford since September 24.
He added: "To be honest, after so many matches playing well but not winning, we need the points more than the performance.
"But I knew against a team like Tottenham it is difficult to get the result without playing well, so we played well. Very well."
