That’s according to former Scotland international Craig Burley who thinks his eight wins from eight games is still not enough.
Tottenham boss Mauricio Pochettino is also in the frame to become Jose Mourinho’s permanent replacement, but Spurs are desperate to keep their manager.
The Argentine will be a costly option and while Solskjaer was only supposed to be a stop gap his stock grows with every win.
But Burley thinks the job will be his if he beats Paris St-Germain the Champions League and finishes in the top four this season.
“If you give me a choice between Solskjaer and Pochettino, it’s a no-brainer”
Burley told ESPN: “I am [changing my mind] a little.
“But again, I think there’s due-diligence that needs to be done.
“If you give me a choice between Solskjaer and Pochettino, it’s a no-brainer.
“But he [Pochettino] may not be available, I don’t know, he might not want it, they might not want him.
“You can’t win eight games and not be at least within a shout. That’s what I’m saying.
“If he knocks PSG out of the Champions League and they get in the top four, I think he’s getting the job.”
Manchester United will look to make it nine wins in a row when they host Burnley on Tuesday.
They beat Arsenal 3-1 in the FA Cup at The Emirates in a thrilling display on Friday night.
He was delighted with the display and praised his players for the way they approached the game.
Solskjaer said: “[It helps] when you’ve got good players, but it’s also difficult to leave them out, it’s much easier to put them into the team.
“It’s hard because you have to think we have the best goalkeeper in the world in David [De Gea].
“Do you leave him in just because it’s a big game? No, because you have to trust all the players in this club.”