Chelsea: Terry not for sale at any price
"We're not going to sell John, so from that point of view it's really irrelevant what another club will offer," Kenyon told Sky News.
He added: "I don't know what they (City) are offering but I'm confident that John is going to remain with us. John is a talisman, he's the heart of Chelsea."
City, who signed Argentine forward Carlos Tevez on Tuesday for a reported 25.5 million pounds, had an offer for the 28-year-old England captain rejected at the beginning of July after originally making contact in January.
"He's too important to us and we're very confident that he'll be leading us forward in the years to come," Kenyon said of Terry.
The signings of Tevez and Roque Santa Cruz have boosted City's forward line and manager Mark Hughes must now strengthen his defence in preparation for a bid for Champions League qualification next season.
Kenyon also added that rather than sell, the west London club could look to sign ahead of next season.
"You're always looking to bring in a bit of freshness and this season is no different. The coach himself would probably like to influence the way we play with another player."