Pogba has been handed the armband on three occasions already this season when club captain Antonio Valencia has been absent, most recently in a man-of-the-match display against Young Boys in the Champions League last week.
However, ESPN reports that the division between Pogba and Mourinho has deepened to such an extent that the manager will no longer consider the World Cup winner as a candidate for the captaincy.
The relationship between Pogba and Mourinho has been under scrutiny for a number of months, and Mourinho's latest action - carried out at Carrington today - is understood to be designed to underline his authority at the club.
The Portuguese is thought to have been angered by comments made by Pogba after various matches already this season, including the midfielder's call for the team to attack more following their 1-1 draw with Wolverhampton Wanderers at the weekend.
Saturday's result has left United already eight points adrift of Premier League leaders Liverpool after only six games of the new campaign.