That’s according to Sky Sports pundit Danny Mills.
Solskjaer replaced Jose Mourinho in December as caretaker boss and has hit virtually unthinkable heights.
With 14 wins in 18 matches, the Norwegian has helped the Red Devils close an 11-point gap in the Premier League top-four race to two points.
And even more spectacularly, United became the first team in Champions League history to lose a knockout first-leg 2-0 and still progress.
The Red Devils won 3-1 away at Paris Saint-Germain in the second leg thanks to a last-gasp Marcus Rashford penalty to set up a last-eight tie with Barcelona.
Club legend Solskjaer – who spent 11 years as a player at United under Sir Alex Ferguson – is loved by the United fans, who can regularly be heard singing a chant in the 46-year-old’s honour to the tune of The Stone Roses.
Recent reports have also indicated that United have already decided that they will officially appoint Solskjaer over the upcoming international break, which comes after they take on Wolves at Moline in the FA Cup quarter finals tonight (7.55pm).
But Mills thinks that United should continue to take their time because Tottenham boss Mauricio Pochettino – said to be the club’s No 1 managerial target after Mourinho’s sacking – could still be a better long-term appointment.
Talking on The Debate on Sky Sports, Mills said: “I still think there’s no rush at the moment [to make a decision].
“Ole’s not going to go anywhere. Even if another club comes in for him at the moment, he’s not going to be going anywhere else.
“Manchester United must still be looking at other candidates. They must be thinking about recruitment, directors of football.
“He’s [Solskjaer’s] done incredible and he’s put himself right in the frame for the job.
“But if Pochettino is on their radar, do you still go with the longevity of what he’s done over a five-year period?
“Buying in players, that’s a big thing. Recruitment is absolutely huge. We don’t know if Solskjaer can do that.
“There’s still a couple of question marks about longevity for him.
“Remember [Roberto] Di Matteo went on and won the Champions League [at Chelsea], made it a happy camp, got the Champions League and got sacked a couple of months into the next season.
“The summer is huge for Manchester United in terms of recruitment, new signings, keeping hold of players, backroom staff and everything else.”