Ferguson, who attended United's 3-1 defeat to Liverpool at Anfield on Sunday, is understood to be a huge admirer of Pochettino, while the pair have met for lunch in the past.
United are now sixth in the table with 26 points from 17 matches.
"The club would like to thank Jose for his work during his time at Manchester United and to wish him success in the future", according to a club statement.
Solskjaer was quickly installed as the favourite to replace Mourinho, with United confirming that they would appoint a caretaker manager until the end of the season. United has already conceded more goals in the league than it did in all of last season.
With all that in mind, here's your chance to have the final say on Mourinho's transfer record at United.
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The 45-year-old is now in charge of Norwegian side Molde, but their season has already finished and does not begin again until March.
It remains to be seen who made the decision first to post and then delete the message, but it is safe to assume Pogba is not disappointed by Mourinho's exit at United.
Do you think United are right to sack Mourinho?
As a manager, he had a disastrous eight-month spell in charge at Cardiff City in 2014 before returning to Molde in 2015 and has just signed a new three-year deal until the end of the 2021 season.
And while some have criticised the former Chelsea and Real Madrid boss, Klopp remains full of respect for Mourinho and all he has achieved in the game.
Jose Mourinho with Paul Pogba as the player was substituted against Leicester in August.
For the first time since leaving Portuguese provincial team Uniao de Leiria for Porto in 2002, Mourinho leaves a club having failed to win a league title.