United face Championship side Derby County, managed by Frank Lampard, at Old Trafford on Tuesday.
Pogba was slammed by his manager during training and told he would never wear the captain's armband again, as he did not have the right temperament for the job.
Mourinho's decision to give Pogba the armband on that occasion came hard on the heels of suggestions Barcelona were pressing to sign the 25-year-old.
United named Antonio Valencia as its captain upon Michael Carrick's retirement after last season, but the Ecuador worldwide has been sidelined by injury.
The World Cup-winning France midfielder subsequently questioned Mourinho's tactics in an interview, suggesting they should adopt a more attack-minded approach at home.
The squad, which includes World Cup victor Paul Pogba and David de Gea, is said to have become a source of frustration for Mourinho following a lack of transfer activity.
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"José Mourinho told the players that Paul Pogba will not be the captain because he doesn't represent what a captain is and Manchester United is bigger than anyone", a Carrington source said, as per The Times.
The game will go straight to penalties if the scores are level after 90 minutes and because of the new rule, and the 1-1 draw with Wolves on Saturday, Mourinho has revealed he is "not thinking too much" about rotating his squad. "Just one decision which I don't have to explain".
However, the game turned inside eight second-half minutes when on-loan Liverpool winger Harry Wilson equalised for Derby and United goalkeeper Sergio Romero was given his marching orders for handling outside the box.
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