The Citizens approached the Chelsea skipper earlier this summer, but the Blues closed the door on a possible switch for the talented center-half.
Apparently, Hughes hasn't given up hope of landing England international Terry this summer, as he asks him to start a 'new challenge' with City.
"We would like to think we could offer him a different challenge," said Hughes.
"From my own experience, when you have been with a club a long time, you maybe get to a point when you need a new challenge, when you think a change of scenery would just re-ignite certain things within you.
Money
"It is not a question of money. It's about a different challenge, a different stage in his life and career, and maybe that's why there hasn't been a response because John is seriously thinking in those terms.
"I went through that process myself and I can understand if that is the way he is thinking.
"We made an offer to Chelsea and I've made known my feelings about John Terry.
"He's an outstanding player and an outstanding person. We'd like the opportunity to speak to him but as yet that hasn't been forthcoming."
Big spenders City have been trying to acquire the services of the 28-year-old since last term.