That is according to former Chelsea forward Tony Cascarino, who believes the interim boss deserves the job on a full-time basis.
Solskjaer has masterminded 10 wins from 11 games since replacing Jose Mourinho in mid-December.
The latest victory – a 3-0 success at Fulham on Saturday – teed them up nicely for tomorrow’s Champions League last-16 tie against PSG.
“Manchester United should give Ole Gunnar Solskjaer the full-time manager’s job,” Cascarino told The Times.
“I understand why they may want to see how the Champions League clash with Paris Saint-Germain goes but he deserves to be given a permanent deal.
“He’s done everything that could have been hoped of him — he’s unbeaten, he’s got the team playing good football, he’s got the star players happy and in form and he’s handling the media brilliantly. He’s made Manchester United a family club again.
“That is proved by Avram Glazer, one of the club’s owners, and the executive vice-chairman, Ed Woodward, going into the dressing room after the win at Fulham.
“As a player that tells you that the manager is being backed by those in power.
“As well as all he has proved so far, there are other benefits with Solskjaer.
“First, the fans would be delighted. Second, he’s a no-risk appointment now — he loves the club and would probably take a two-year deal without much drama or fuss.
“Then if it didn’t work out and his current success is just a flash in the pan then it’s no major issue to say thanks for everything and sack him. He’d still be considered a club legend and the fans would be glad he was given a chance.
“The only other option for the club seems to be taking Mauricio Pochettino from Tottenham, which would be very expensive and comes with no guarantees.
“Solskjaer was a surprise pick as interim manager but we shouldn’t be surprised if he stays.”
United poached Solskjaer from Molde until the end of the season and it has been suggested a full-time agreement is already in place.
But, speaking in January, Molde managing director Oystein Neerland said: ”The deal is until May 12. That is our Plan A and our Plan B. We have no Plan C.
“We have only spoken with United about this period, January to May. Nothing else. I’m staying with this plan.”