There have been two arrivals at Old Trafford so far in this window – Daniel James and Aaron Wan-Bissaka – but more signings are expected by August 8.
A new central defender is wanted to partner Victor Lindelof at the back while Solskjaer wants at least one new central midfielder.
Starsport understands Leicester City ace Harry Maguire is the centre-back being eyed by the Manchester United boss.
Ed Woodward remains locked in talks for the England international, who is valued at £90m by the Foxes.
Sean Longstaff, the Newcastle United prospect, is wanted by Solskjaer to strengthen the team’s engine room.
The departure of Ander Herrera has left United short of options in the middle.
According to the Evening Standard, Solskjaer has not been deterred by Newcastle’s £50m valuation of Longstaff.
The Norwegian had hoped to complete the club’s business before their pre-season tour of Australia and Asia.
Solskjaer, however, claims he is content with the business and has pleaded with fans to be patient over further arrivals.
“I’m very happy with the two players we’ve brought in, but now we’ve got to be patient,” he said.
“This is a long haul and it is very important we get the right ones in.
“We can’t just jump onto a different path if we hit a hurdle. My feelings are that I am not frustrated at all.
“I believe in these players. I’m sure we could do well but it’s both short-term and long-term.
“We’re working on something we’ve identified that cold improve us, but we’ve played well, performed well, had some good results so far.
“But it’s not about winning games in pre-season. It’s about finding a way we want to play to get to the starting line and the team to be gelling.”
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