United have been in fine fettle since the arrival of Solskjaer, who has lifted the spirits of the club after a gloomy season under Jose Mourinho.
Under the Norweigan, they have found themselves back in the race for the top four – battling with the likes of Arsenal and Chelsea.
And they remain in the Champions League despite a tough draw with Paris St-Germain, coming back from 2-0 down to knock out the French champions at the Parc des Princes.
This has impressed the Old Trafford officials, who are now moving away from previous top managerial targets Mauricio Pochettino and Massimiliano Allegri.
United have now opened talks with Solskjaer’s agent Jim Solbakken over the role as permanent manager, according to the Evening Standard.
The negotiations are set to take place over the next two weeks, with a decision set to be made at the end of that time period.
Solskjaer has placed himself as the favourite for the job after completing a number of objectives and excelling in many of them, too.
The former Cardiff boss was expected to just steady the ship until the end of the season.
With a huge summer planned, United chiefs are keen to clear up the issue surrounding the managerial hot-seat and have instructed intermediaries to distance the club from Pochettino and Allegri.
The former has been a top target of United as well as Real Madrid in the past but the Argentinean would take a hefty fee to prise away from Tottenham.
And Allegri has put contract talks with Juventus on hold as he considers his options.
But the Evening Standard report that Solskjaer’s effect on the supporters and the Glazers has been a key reason behind the decision to open talks with the club legend.
And his relationships with players has been one of the catalysts for the club bringing forward talks.
A number of first-team stars have spoken out on their adulation for Solskjaer, including Paul Pogba, Jesse Lingard and Romelu Lukaku.
“Of course we want him to stay,” Pogba said of Solskjaer. “The results have been great. I have a great relationship with him, he has a great relationship with the players.
“When a player is happy, he wants to keep being happy. Solskjaer deserves it. He knows the club, he knows everything about the club.
“He is a really happy coach that gave confidence back to the players.”