Reports this week have claimed Solskjaer wants to keep Lingard until the end of the season as United continue to challenge on three fronts.
The Norwegian was asked specifically about Lingard, and while refusing to name the Englishman, he said it was possible some players could leave Old Trafford.
"I don't want to go into individuals," Solskjaer told reporters. "We can allow maybe one or two more to go out.
"But then, it's one of the strengths we have, is that we have had a deep squad with strength and depth. We don't want to give our advantage away by easing off on our players, so I can't really give you a better answer than that."