United could be without five members of their first-team squad for the trip to face Sociedad.
The Red Devils will be without Paul Pogba, Donny van de Beek and Edinson Cavani, and could be without Anthony Martial, too.
Martial and Scott McTominay both pulled up with slightly injuries during training this week, giving Solskjaer a fresh injury headache.
Both will travel to Turin with the rest of the squad for the match, and will be evaluated beforehand.
The same can’t be said for Cavani and Van de Beek, however.
Both will miss out after suffering knocks earlier this week, and neither will travel with the team.
That gives Solskjaer something of a dilemma with his team selection, as he could be without a recognised striker.
As a result, Marcus Rashford could lead the line and free up a spot for new signing Amad to make his debut.
Elsewhere, Pogba may not play again this month as he continues his recovery from a thigh injury.
The Frenchman has been key to United’s recent good form but Solskjaer will have to do without him against Sociedad.
Speaking at his pre-match press conference, the Norwegian boss confirmed Pogba is still yet to come back to full training after his thigh issue.
“With Paul, he’s recovering well,” Solskjaer said.
“He’s starting the treatment and will still be a few weeks, he won’t be playing in February, that’s for sure. So still a few weeks until we see Paul, definitely.
“Apart from that, we have a couple of doubtful ones [to see] if they’ll be fit enough. Anthony and Scott, we’ll have to check them tomorrow. Edinson and Donny definitely not travelling.”