Chelsea chief executive Peter Kenyon told Sky News: "I don't know what they are offering but I am confident John is going to remain with us.
"John is the heart of Chelsea, he is our captain and has also become captain of England while he has been here. We are not going to sell John, so it is irrelevant what another club will offer," Kenyon went on. "We are very confident he will be leading us in the years to come."
City have reportedly offered the 28-year-old, who still has three years on his Stamford Bridge contract, a staggering £200,000 a week to sign a deal which would see him join Gareth Barry, Roque Santa Cruz and Carlos Tevez who have cost City £50 million in total this summer.