Earlier in the close-season, United captain Harry Maguire was handed a suspended 21-month sentence by a Greek court after being found guilty of assaulting a police officer, resisting arrest and attempted bribery during an incident on the island of Mykonos.
Maguire denied the offences and has launched an appeal which nullifies the conviction, but the defender still lost his place in the England squad for the Iceland and Denmark matches.
Confident Maguire can focus on football despite the off-field distraction, Solskjaer said: "The process will keep on going. Knowing Harry, he's a very strong character so hopefully he can put that apart.
"Naturally, as a human being it will be in the back of his mind what's happened this summer, and apart from that you've just got to see how it develops."
United have spent most of the close-season in an unsuccessful attempt to sign Borussia Dortmund forward Jadon Sancho.
The deal is still not completely dead according to reports, but Solskjaer would only confirm that United are still looking to strengthen after signing just Ajax midfielder Donny van de Beek so far.
"You know I can't say anything about other clubs' players out of respect to them. I can't speculate. But we understand that to get even further; one - we need to develop what we have, two - we're also looking to strengthen the team, of course we are," Solskjaer said.
"I've been in dialogue with the club. Of course, we're always discussing and hopefully let's see if we can bring anyone in."