The Old Trafford giants are top of the Premier League at this stage of a season for the first time since Sir Alex Ferguson retired, and also remain in the hunt for FA Cup and Europa League glory.
But Solskjaer is not expecting any additional faces to boost United’s bid for silverware before the February 1 transfer deadline.
“I wouldn’t think so, no,” the Norwegian said. “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.”
United have brought in one new player this month but it remains to be seen when highly-rated Amad Diallo will be involved in a first-team matchday squad.
The Old Trafford giants reached an agreement with Atalanta for the 18-year-old in October, with the winger completing his £18.7m move in January – a deal that could reach £36.5m.
Asked if Diallo has the potential to be a long-term solution to United’s right wing issues, Solskjaer said: “Well, that’s his preferred position. He’s clever at finding space.
“He can go inside and outside. He’ll get the time to prove that he is the one.
“Of course along the way we’ve got Mason (Greenwood), Marcus (Rashford) who’s played out there, Dan (James), Juan (Mata) so we’ve got options.
“Paul (Pogba) has played there but I think when you look at the squad and you look at Amad you think yeah, that’s probably where we’re going to work to fit you in.”
Solskjaer says it will not too long until Diallo is involved, but fellow teenager Facundo Pellistri looks set to leave to get some much-needed first-team experience.
“There has been talks and there’s been quite a few clubs interested in Facundo to go out on loan and that’s maybe something we will let him do now,” Solskjaer said of the 19-year-old, who has yet to make his debut since leaving Penarol for £9m in October.
“He’s had a few games in the reserves. We want him to have regular football, of course, at a high level of course.
“With Amad, I think it’s a different scenario. He’s just come in, he’s going through a good training regime and training programme and he’s doing well. It won’t be too long, I feel, before I can bring him into the squad.”
In terms of outgoings, Timothy Fosu-Mensah has already this month completed a permanent move to Bayer Leverkusen and Odion Ighalo’s loan from Shanghai Shenhua expires on January 30.
The striker said on Twitter: “It’s so hard to see this dream come to an end.”
Marcos Rojo and Sergio Romero have been told their deals will not be extended beyond the summer, while home-grown full-back Brandon Williams has been linked with a temporary exit in search of first-team minutes.
The PA news agency understands there has been interest from home and abroad in a loan deal for Jesse Lingard, with a switch to West Ham reportedly in the offing for the out-of-favour England international.
Asked about the situation with Williams and Lingard, Solskjaer said: “They’re still part of the club, part of the squad, training well. No deal has been struck for any of the players yet going out – still a little period left, of course.
“There’s been many clubs interested in our players, so let’s see what happens.
“For me, it’s also important to take our wishes and our plans into consideration but also the players of course, because they are Man United people and players through and through.”