The Red Devils turned to their former striker to take over the reins from Jose Mourinho in a temporary role following the Portuguese coach’s dismissal after a 3-1 loss at Liverpool FC in December.
However, Solskjaer has surprised his critics by masterminding a brilliant 12-game unbeaten run in all competitions to close the gap on the top four despite being handed the job with Manchester United 11 points adrift of fourth spot.
The Red Devils were brilliant 3-1 winners against Arsenal in the FA Cup fourth round at The Emirates to set up a sixth-round tie against their top-four rivals Chelsea FC at Stamford Bridge on 18 March.
Before that cup tie, Manchester United have the small matter of the first leg of their Champions League round of 16 clash against Ligue 1 holders Paris Saint-Germain at Old Trafford on Tuesday night.
In what promises to be a decisive part of the season for Solskjaer and his players, Manchester United will welcome Liverpool FC to Old Trafford on 28 February as they look to halt their rivals’ title charge.
Former Manchester United defender Neville believes Solskjaer has a chance to make himself the clear favourite to get the Old Trafford role on a permanent basis.
“If they beat Chelsea, beat PSG, beat Liverpool, Solskjaer is absolutely in the box seat and you’d be saying, ‘How can you not give it to him?’,” Neville told Sky Sports.
“The club have appointed two big names with the last two appointments and it hasn’t worked out.
“The idea of Ole going through that run of fixtures and coming out of it well, you couldn’t sit here conceivably and see another manager. But I think Ole himself will think, ‘Let’s get through February and March and if I’m doing what I’m doing now, I’ve staked a claim’.
“At this moment he is staking a claim but he knows there is massive challenges to come.
“The job that Ole is doing now is exactly what the club asked him to do – to get the club happy again on and off the pitch.
“However, is he the man to win them the Champions League and the Premier League? If the answer to that is yes, then they should give him the job.”
Manchester United have beaten Arsenal and Tottenham during their impressive unbeaten run under Solskjaer so far.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news