Mourinho, who yesterday described himself as the Happy One rather than the Special One, said Terry would stay club captain, but only if he plays.
Asked about the former England captain's lack of involvement under Benitez, Mourinho replied: "I don't speak about a club when I leave, and when I arrive at one I don't like to comment on what happened before me.
"What I can say is about the future, and the future is to meet John in the first week of July and try to get the best out of him.
"I know what he can give. Let's try to make him again a very important player that he couldn't be last season.
"With the armband, he will wear it if he plays. If he isn't in the starting XI then he won't wear it."