Ole Gunnar Solskjaer has been appointed as Uniteds interim manager until the end of the season, while Mike Phelan has also been brought in to assist the Norwegian.
But United will be seeking a long-term replacement for Mourinho, who was sacked after a brief meeting at the clubs training ground on Tuesday morning.
Several candidates have been linked with the role including Pochettino, Zinedine Zidane and Antonio Conte.
But according to The Sun, Ferguson has been championing Pochettino to Uniteds hierarchy and wants the Spurs boss to land the role.
United, however, face a difficult task of landing Pochettino from Tottenham.
The Argentine signed a new contract with Spurs in May which keeps him tied to the club until 2023.
And it will cost United around £34 million in compensation.
On Tuesday, reports claimed that Pochettino wants to be considered for the United job and considers the chance too good to turn down.
it was also claimed that United are preparing an offer to Pochettino as well as his Spurs coaching staff.
Elsewhere, Conte is interested in managing United if the club fail to prise Pochettino away from Tottenham.
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