That’s according to Sky Sports pundit and United legend Gary Neville.
The Red Devils are unbeaten in 11 games under caretaker boss Solskjaer, who has overseen 10 wins and a charge up the Premier League table.
United were 11 points off of fourth when the Norwegian took over but leapt above Chelsea thanks to their 3-0 defeat of Fulham at the weekend and now occupy the final Champions League qualification spot.
Solskjaer has amassed 25 points in just nine league games with Mourinho having managed 26 in United’s first 17 top-flight matches this term.
It was initially suspected that United would look to prise Mauricio Pochettino from Tottenham in the summer to be their new permanent manager.
But club hero Solskjaer is certainly stating his case to be a serious rival to the Argentine for the position with United on form for a top-four finish and full of confidence headed into a Champions League last-16 showdown with Paris Saint-Germain and an FA Cup fifth-round tie with Chelsea.
And after the United away end at Craven Cottage serenaded Solskjaer throughout their win, in which Paul Pogba bagged a brace, former right-back Neville thinks the supporters are making it known to the club’s hierarchy what decision they want them to make.
“I genuinely did think it would be a five-month interim period where he would come in and bring everybody together and get everybody happy,” he told the Gary Neville Podcast.
“The whole club loves him, he’s just a fantastic person. The players have responded to him, the fans love him to bits.
“They continued to sing his name all the way through against Fulham, it was incredible.
“The fans are almost in some ways determining the outcome for the board, because you can’t go against that support, that fan base is incredible, it’s huge and they love Solskjaer.
“What they’re seeing, they like. I still think there’s no need to announce anything today because the minute Ole gets the job, it’ll be, ‘Right who are you going to sign? Who are you going to get rid of?’
“It’s a different type of questioning. At the moment it’s still a very good atmosphere. Once the actual job does come if it were to come, the questions would start to change and become a lot more serious.
“He’s almost got a free hit at the moment because it couldn’t get any worse in terms of the mood, now it’s not just an increased level of happiness but genuinely top performances.
“If you look over the last seven or eight games, even the Burnley, coming back from 2-0 down, was something to be admired.”
And Neville believes that Solskjaer has such credit in the bank that his chances of landing the job are not dependent on United’s results in the Champions League or FA Cup, but rather the manner of their performances.
He added: “I’m looking at it from an owner’s point of view or boardroom point of view. If United continue in the vein that they are towards the end of the season, playing the way they are, the feeling is as good as it is, they get into the top four, the risk of not giving Solskjaer the job is huge.
“If next October they’ve spent £30-40million to get a manager and a new coaching set-up into the club and they’re fifth, all hell will break loose because they’ll say, ‘How the hell did you not give the guy the job who was doing it well?’
“All Ole has to do is continue in the same vein. He doesn’t have to go out and beat PSG or have to go and beat Chelsea. The way in which they go out is important]., if they were to go out to PSG or Chelsea.
“As long as the nature of the performances and the feeling continues, if you come out of that in four, five, six weeks time, United are in fourth – if they’re still in the Champions League and FA Cup at that time it’s a no brainer – but if they’re out of those competitions I still don’t think it’s a case of saying Ole shouldn’t get the job because of that.
“It’s more about the nature of what’s continuing. The reality is it’s too big a risk to sit here next October or November having put a new manager in charge if the manager at this moment in time is delivering title-winning results.
“You think the last nine or 10 games, United are top of the form table. If you can continue that, why wouldn’t you [hire him]?”