Pogba returned to Old Trafford from Juventus in 2016, with huge expectations following his a trophy-laden stint in Serie A but the France international has struggled to make a notable impact.
Reports in English media claim Mourinho and the enigmatic midfielder's relationship has reached breaking point over the apparent contrast in tactical agendas and character, but Drogba has dismissed the notion.
The former Ivory Coast striker believes the Portuguese tactician is simply challenging the talented midfielder to rise above his slump in form at the Theatre of Dreams.
"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."