Hodgson has indicated he already knows who will take on the armband, with both veteran midfielder Frank Lampard - who left Chelsea to join New York City FC before being loaned back to parent club Manchester City - and forward Wayne Rooney, the new Manchester United skipper, the leading candidates.
While not wanting to draw any direct comparisons between the contenders, Mourinho has no doubts centre-back Cahill could perform the role if asked.
"I don't want you to say that I prefer Gary in front of Rooney or Gary is better than Rooney. No, I just speak about Gary and Gary can be a captain," said Mourinho.
"He is not the captain here because we made the decision that John (Terry) is the captain for many, many years, and after that it is about years at the club, so Petr Cech, Didier Drogba, Branislav (Ivanovic), (John) Obi Mikel, so he has lots of guys in front of him.
"So is he going to be Chelsea captain? I hope not, because for him to be (Chelsea) captain then five or six of the other guys they are not able to play.
"But can he be a captain, do I feel he has the captain's profile? Yes."
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- Wayne Rooney
- Steven Gerrard
- Roy Hodgson
- Frank Lampard