United are still thought to be in hot pursuit of Borussia Dortmund winger Jadon Sancho, while Real Madrid left-back Sergio Reguilon is also on their radar.
Van de Beek cost United £35.7million and Solskjaer admitted United would not be spending as much as Premier League rivals Chelsea, who look set to exceed the £250m spend mark.
However, they are still hoping to do some business this summer if they can identify the right fits.
‘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,’ Solskjaer told BBC Five Live.
‘This summer and year has been a strange one and it is very important everyone understands this has an affect on football. Not everyone can spend millions and millions.
‘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 develops.
‘We are developing team, a year or so into our rebuild. We had to make some decisions last summer and throughout the season we have seen how this team is getting better and getting used to each other.
‘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.’