After suffering their worst start to a Premier League campaign in 28 years, Jose Mourinho was sacked in mid-December with 26 points from 17 games.
Solskjaer arrived as interim-manager with the club reportedly intending to target Tottenham manager Mauricio Pochettino at the end of the season.
However, after lifting United back into the top four with 25 points from his first nine league games, it's been reported by Sun Sport that the Norwegian will be given the job on a permanent basis at the end of the current season.
The report states United will continue to 'publicly stick to the mantra' that the search for Jose Mourinho’s permanent successor remains 'ongoing'.
But the hunt is over with co-chairmen Joel and Avram Glazer now convinced they have the right man in Solskjaer after attending the 3-0 victory over Fulham at Craven Cottage on Saturday.