The Frenchman, who re-joined United from Juventus in a world-record move in 2016, has struggled to make an impact at Old Trafford.
Reports in the English media claim that the relationship between the manager and Pogba has hit an all-time low, but Drogba believes the Portuguese tactician is merely challenging the midfielder to raise his game.
“It’s been hot between us [Drogba and Mourinho],” Drogba told ESPN.
“But Jose is never going to attack people he does not like. He likes Paul a lot.
“That’s why he’s given him a lot of responsibilities.”
Pogba will look to return to form for United when they host Swansea City in a Premier League clash this Saturday afternoon.