The search for another forward appeared to be over after Odion Ighalo's loan was extended to January 2021.
"You need competition for places at Manchester United," Solskjaer told a press conference before Tuesday's clash with Brighton.
"If you think you've got a divine right to be playing every game and are doing so well that we're not going to look for players to replace you, you're in the wrong place.
"We've always got to look at improving, and if they don't improve, we might have to look somewhere else to get better because we have to be better. We're too far away from where we need to be and want to be."