The interim manager has been offered the cash by executive vice-chairman Ed Woodward to strengthen his side’s defence.
But Solskjaer has prioritised the signing of attacking players over new defenders.
Victor Lindelof struggled in the recent 2-0 against Arsenal as the 24-year-old put in one of his worst performances of 2019.
Chris Smalling was the calmer of the two centre backs, and Solskjaer believes both deserve more chances to prove themselves.
United were heavily linked with a move for England World Cup hero Harry Maguire last summer.
But Woodward denied former boss Jose Mourinho the required funds to sign the defender from Leicester.
And ironically, now that the Old Trafford chief is willing to splash the cash on a defender, United’s current manager has no intention of doing so.
News of Woodward being prepared to splash the cash this summer come amid:
According to The Sun, Solskjaer’s priority is a right winger who can score as well as supply goals for Marcus Rashford.
United are interested in bringing Jadon Sancho back to the Premier League from Borussia Dortmund where he has excelled.
The Norwegian manager is also monitoring Juventus star Douglas Costa and Inter Milan wide man Ivan Perisic.
Luke Shaw has been highly impressed by Solskjaer for the positive impression he has made on the United dressing room.
Not only have results dramatically improved under the former striker, but the entire mood around Old Trafford has also been lifted.
“It’s really positive, the mood in the camp is so good at the moment,” Shaw told Premier League Productions.
“It’s really enjoyable to be around it, and all the positive stuff is, I feel, showing on the pitch with each player. Especially the ones that have come in and taken their chances.
“With the injured ones, I think everyone is trying to stake a claim for their name on the team sheet.
“I think that’s showing in the results, and that’s only good for us to have that competition in the team.”