The Norwegian, who joined United in December on a caretaker basis, signed a three-year contract to confirm he will remain in charge beyond this season.
The 46-year-old plans to move into the house he bought 12 years ago in his final year as a United player, but Van Dijk has been living there since he joined Liverpool from Southampton in January 2018.
Although Solskjaer is excited to finally take up residence in the Cheshire home, he suggested at a press conference on Thursday that he will not force the Dutch defender out prematurely.
Asked if he has told Van Dijk he needs to leave, Solskjaer replied: "No, I haven’t. We’ve got a contract there."
Solskjaer's family have been living in Norway because of the former striker's short-term deal at Old Trafford, but he told MUTV that they will soon be reunited.
"We’ve really enjoyed the last eight years living in Norway. It’s going to be a change for them but we’re looking forward to it," he said.
"The six months that we agreed on [until the end of the season] as a family we agreed to do it separately as there was no need to move them over. That’s gone now. Now we’re moving together.
“We built a house, or I started it in 2007, but finally maybe in 2019 we can move into it – that’s long planning!"
United have won 14 of the 19 games they have played since Solskjaer replaced Jose Mourinho at the helm, reviving their challenge for a top-four finish in the Premier League and progressing to the last-16 of the Champions League.
The former Molde boss has set his sights on leading United to a Premier League title and says the club will start working on strengthening the squad through summer transfers before the end of the season.