Solskjaer plans to sign a striker on loan after confirming Marcus Rashford has suffered a double-stress fracture of the back.
United have been rocked by the loss of their leading scorer for up to three months.
The United manager said: “We've had many, many injuries this season, it's an unfortunate situation.
“The window is open so we might look at some short-term deals to get us through to the summer."
Solskjaer added: “The players are giving absolutely everything. When you miss Scott, Paul, Marcus - any club and any team will notice that. So that might mean that we might look at some short-term deals to take us to the summer.
“The permanent signings we are looking for, the targets are not going to change because we've got two or three players injured for the next few months. It still has to have a plan behind them.
“But there might be some short-term deals that we have to do."
While he hopes to bring in cover, Solskjaer admits United will have to rely on 18-year-old Mason Greenwood in Rashford's absence.
“We've just got to (cope) for a while," he added. “He's been absolutely fantastic all season.
"We had a similar spell with Anthony out for eight weeks and Mason had a few games and now he's got a few more games. Juan (Mata) is getting back to his best, so we will just have to deal with it.
“We've been careful with him (Greenwood) because he's a top player and this is a chance for him. But it might be that we do one or two things in the window."