Pogba was last in action for France in their 4-2 victory over Sweden during the international break this month and missed United’s 1-0 league win over West Bromwich Albion and Tuesday’s 4-1 Champions League victory over Istanbul Basaksehir.
The 27-year-old had missed a large part of last season with an ankle injury and Solskjaer said that his current problem is not a recurrence.
The manager added midfielder Scott McTominay was also doubtful due to a knock.
“Scott McTominay and Paul Pogba weren’t on the grass, so they’re unlikely for weekend,” Solskjaer told reporters.
“Luke Shaw (hamstring) just started rehabilitation. Jesse Lingard is back with the group after isolating and Phil Jones (knee) still out until after Christmas.”