Former United striker Solskjaer has made an excellent start to his temporary spell in charge at Old Trafford, winning eight and drawing one of his first nine games.
The Norwegian was not thought to be a candidate for the permanent post upon arrival but the United hierarchy are now seriously considering him in the search for Jose Mourinho’s successor.
Solskjaer has made no secret of his desire to take the job, despite the fact that he is due to return to Norway with Molde at the end of the season.
Molde’s co-owners, Kjell Inge Røkke and Bjørn Rune Gjelsten, know that the United job is Solskjaer’s ideal role and wished him 'good luck' back in December, telling him not to return.
Solskjaer said: “When I rang the owner and said that United had called and that he always knew that this had been my dream, he said: ‘Go over, enjoy yourself and please don’t come back.’
“Both owners wished me all the best because they knew this is something I dreamed about.
“To get the backing from them was fantastic. If I go back to Molde, I will do my best for them but it depends when I go back.
“It’s been fantastic so far. Hopefully I will get to see my family soon, because that has been the only downside to the job.”
Solskjaer's family have remained in Norway since he accepted the caretaker role, though visited Manchester at Christmas shortly after his appointment.
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