The 31-year-old England skipper -- who on Thursday had said he didn't pay any attention to outside criticism of his form -- has failed to sparkle and was anonymous in the two Premier League defeats United suffered last week.
Mourinho, who himself has been subjected to criticism after United slumped to three successive defeats last week -- his worst run since 2002 -- would not, unlike his predecessor Louis van Gaal, guarantee Rooney a starting place.
"Wayne is the captain of the club, the manager and the players -- he is trusted by the players, he is trusted by myself and he represents the club in a fantastic way as a player and person and what is now socially," said Mourinho.
"Football is a different story.
"Football everyone is the same and if he has to go on the bench, he goes on the bench.
"If he has to stay at home, he stays at home, but that doesn't mean that you don't trust him or you have a problem (with him). Not at all.
"We have no problems. He is our captain but, of course, no privilege, he is like anyone else."
Mourinho, though, believes that Rooney's form or certainly morale has dipped since he was heavily slammed for his performance in the 2018 World Cup qualifier with Slovakia earlier this month which England won 1-0 with a late goal.
"Honestly, I think there was a Wayne before the Slovakia-England and a Wayne after the Slovakia-England," said Mourinho.
"And I am not blaming Sam (Allardyce, the England manager), not at all.
"I am blaming the people that after the England-Slovakia was, in my opinion, too strong with somebody that is a very important player in the history of English football, is the captain of England, is the record of goals, is almost the record of matches.
"I think it was too much but I still think, that a big boy like he is, he has to face it in a strong way."
Mourinho, who righted the ship slightly with a League Cup win over third-tier Northampton Town on Wednesday, said Rooney had faced down his critics before.
"That's what he tries every time. When he is on the pitch, he gives 100 percent. Always, always," remarked Mourinho.