United have made one signing since finishing third in the Premier League last season, bringing in Donny van de Beek from Ajax for a fee that could rise to £39.1million (€44m).
Borussia Dortmund attacker Jadon Sancho is widely considered to be a primary target for Solskjaer, but United have been unable to reach an agreement with the German club.
Left-backs Sergio Reguilon and Alex Telles have also been linked, though Solskjaer is adamant his side will not pay over the odds for any targets in the current market.
“We are always looking to see if there is any way possible that we can improve this squad and bring players in that will have the right level, quality, personality and fits all the criteria,” he told BBC Radio Five Live.
“This summer and year have been a strange one and it is very important everyone understands this has an effect on football. Not everyone can spend millions and millions.”
“It is never easy to have too many new players in the team, it takes time for players to gel into a unit.”
“We have seen some clubs go for the quick fix and some have trust in the process. We have to improve and get results but adding players with different qualities than we have.”
When asked how many more signings he would like to make before the transfer window closes on October 5, Solskjaer said: “I never set myself a target, like scoring 20 goals as a player.
“You just have to go day by day, making sure you develop and improve. We have a vision of where we want to get to but know so many things can come in the way. I believe in seeing how the team and club develop.”
United could well go into their opening Premier League game against Crystal Palace next week with Van de Beek as their only new recruit.