That is the opinion of Paul Merson, who also believes they should not sign Jadon Sancho.
The Red Devils have signed their first player of the summer after the arrival of Van de Beek from Ajax.
The Netherlands international has penned a five-year contract, with an option for another season.
However, Solskjaer is still in the market for more players with his sights set on a defender and a right-winger.
And Merson reckons the Norweigan should have prioritised his defence going into the remaining weeks of the transfer window.
"Donny Van de Beek looks like a panic buy at Manchester United," he exclusively told Starsport
"I don’t get it. They just spent £40m on a position where they are already strong.
"And how does he play with Paul Pogba and Bruno Fernandes?
"You have to have someone who can play the holding role.
"That signing looked to me like: ‘Oh we haven’t bought anyone yet, let’s go and buy someone, who can we get?’
"When you look at their midfield, Fred was improving, and they’ve got Scott McTominay. Now they won’t get a game.
"And they just gave Nemanja Matic a new contract. "Would they have done that if they knew they were getting Van de Beek?
"It makes no sense to me. Who is making these decisions?
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"It’s like them going for Jadon Sancho. If they sign Sancho, Greenwood doesn’t play. For me they need another centre back."
As well as Sancho, RB Leipzig star Dayot Upamecano has also been touted for a move to United.
Solskjaer is desperate to partner Harry Maguire at the back after being less than impressed with Victor Lindelof.