United finalised the initial £19m signing of Amad Diallo last week having arranged a deal during the final days of the summer window, but that is likely to be their last foray into the winter market.
Solskjaer otherwise expects to trim his squad down this month, with Sergio Romero, Marcos Rojo and Timothy Fosu-Mensah all told that they can leave the club this month ahead of their contracts expiring this summer.
“I think the signings we made in the summer strengthened the squad really well, good signings and good characters and good players,” Solskjaer said.
“January is always difficult. If something comes up that is a long-term target anyway that is another scenario. But not many teams would like to lose players in January.
Solskjaer added: “It's unlikely something will happen on the 'in' side. There might be two or three going out because they deserve to play more football for their own good and their own careers.”
The signing of Diallo - which could rise to £37.2m in add-ons - followed those of Donny van de Beek from Ajax, Alex Telles from Porto, Edinson Cavani as a free agent after leaving Paris Saint-Germain and young winger Facuno Pellistri from Penarol.
United can move to the top of the Premier League table for the first time this season by avoiding defeat to Burnley in their game in hand over leaders Liverpool on Tuesday night.