The Red Devils are competing at the top end of the Premier League for the first time in several seasons.
While the fans may want to see the squad strengthened, Solskjaer suggested any moves will be very difficult this month.
"I wouldn't think so, no," the Norwegian told reporters about new signings.
"I'd be surprised if we do any incomings.
"The squad is strong, it's full of quality. I still need to leave players out for the squad at times.
"Bar something surprising happening, I wouldn't think something will happen (in terms of) incomings, no."