The Red Devils revealed on Sunday that they would be looking for an interim manager for the remainder of the season after Ole Gunnar Solskjaer's departure as head coach.
However, it has since been widely reported that the club are keen to appoint their first-choice target Pochettino in the coming weeks.
According to ESPN, the 20-time English champions have already approached PSG to discuss the Argentine but have seen their initial enquiry knocked back.
The report claims that the Ligue 1 giants are not currently willing to allow Pochettino to leave, with the South American having a contract in Paris until June 2023.
Michael Carrick is currently in charge of first-team affairs at Old Trafford and led the team to a 2-0 victory over Villarreal on Tuesday, which secured their spot in the last-16 stage of the Champions League.