United fell to a 2-0 loss at Arsenal on Thursday , left in fifth in the Premier League table and sitting five points behind fourth-placed Chelsea.
Central midfield is an area of huge concern at United, with Paul Pogba (ankle) and Scott McTominay (knee) set to be sidelined for several weeks.
Solskjaer said he would like to make signings, but added it would only be if United could find the right players.
“You can see the squad and sometimes you think, yeah, one or two additions would do nicely because we are building towards something,” he said.
“It just depends on if what we think will be right for us will be available. Of course it’s playing on our decision-making when we’ve got two players out for a bit, Scott for two months and Paul for a month.
“That gives us less options and we have loads of games and important games.
“But it still has to be right and that’s the big point here, if someone is available and something is possible we’ll do it.
“We’re looking at one or two.”
United are back in action on Sunday , making a trip to Wolves in the FA Cup third round
Ole Gunnar Solskjaer hinted at January signings for Manchester United
117