Manchester United have completed deals for Tom Heaton and Jadon Sancho ahead of the start of the season.
United have also agreed a fee with Real Madrid for Raphael Varane, and an announcement is imminent.
United have been linked with some other transfer targets, although it seems Solskjaer may just be done for the summer.
However, Solskjaer confirmed that the confirmation of Varane is set, but also hinted that Manchester United may not be done yet with signings.
Asked if there could be more new signings at Old Trafford before the window closes, the United boss told Sky Sports: “You never know what’s going to happen in football.
“Of course we’ve still got one hopefully coming in [Varane] and any surprises, anything can happen. We’ve got to be ready. But I’m very happy with what we’ve done so far.”