The £35m summer signing from Ajax is yet to start a Premier League or Champions League game for United with the likes of Paul Pogba, Bruno Fernandes, Fred and Scott McTominay preferred to date.
Though Van de Beek has appeared in all seven of United's games in the opening weeks of the new season, his only starts have come in EFL Cup wins over Luton Town and Brighton and Hove Albion.
Solskjaer said that he has many options available to him in midfield and, though Van de Beek is fit for selection, the 23-year-old is also still adapting to his new surroundings.
"Donny's fit enough but of course it's competition for places, it's giving him time to settle in and adjust to his new teammates, it's a new league," Solskjaer said.
"He's an absolutely top footballer and top personality, so humble and hard-working but also he’s of course eager to play more.
"You'll see him throughout the season, it’s going to be a long, long season and you'll see him. He’s impressed me."
Van de Beek's lack of playing time was called into question by Sjaak Swart, the former Ajax winger who now works as an adviser for the United player's representatives.