According to the Mail on Sunday, Ferguson was saddened not be approached by the club’s hierarchy over the appointment of the new Old Trafford boss.
Following Jose Mourinho’s dismissal in December, Solskjaer was given the job until the end of the season to get the club back on track.
The Norwegian hit the ground running in charge, winning his first eight games, and also led his side to a stunning Champions League victory over Paris Saint-Germain to progress to the quarter-finals of the competition.
However, United succumbed to another barren patch of form towards the end of the season, losing eight of their last 12 outings in all competitions.
Solskjaer was handed the full-time job back in March and was given a three-year deal to steer the club back into the right direction.
The Mail on Sunday state Ferguson was keen on the club hiring Tottenham boss Pochettino before Solskjaer was given the contract.
The Scot is said to be a huge admirer of Pochettino, who has guided his side to a Champions League final this season despite signing just one player in the past three transfer windows.