Micah Richards has made nearly 250 appearances for Manchester City since his debut in October 2005, but the longest-tenured player on the club has turned down their offer of a new contract.
Pablo Zabaleta has established himself as Manuel Pellegrini's first-choice right-back over the last two seasons instead of Richards.
City will want around £7 million for Richards, who won't turn 26 until June.
Richards has been linked to Arsenal if Bacary Sagna leaves as widely expected.
Richards has also been linked to Liverpool and Newcastle.