Solskjaer has not ruled out forgotten man Lingard leaving the club before the window shuts.
Speaking after United's 3-2 FA Cup win over Liverpool on Sunday, Solskjaer said: "Of course, he wants to play football and we'll have to sit down with Jesse and make a decision.
"He trained this morning with a small group who weren't in the squad. I'm very happy to have Jesse around us but he is the ultimate professional.
"I know that he was ready to play today and would've played well."