It is understood that the decision has been made at board level, but may not be announced until the end of the season.
Co-chairman Avram Glazer spoke with Solskjaer after United’s 3-0 win over Fulham, and is said to be convinced alongside fellow co-chairman Joel Glazer.
Tottenham manager, Mauricio Pochettino, had been United’s main target for the job, with Ed Woodward trying to lure him away from North London for next season.
And it appears United will still maintain that the search for a new manager is ongoing, despite new reports to the contrary.
But since being named interim manager following Jose Mourinho’s sack, Solskjaer has won 10 of his 11 games in charge and is yet to lose.
This run of form has seen United rise to fourth place in the Premier League, one point ahead of Arsenal and Chelsea.