The 26-year-old defender is out of contract at the Etihad Stadium this summer and has been linked with Aston Villa.
Richards joined City as a 14-year-old from Oldham and, after making his debut in 2005, went on to play key roles in the FA Cup and Premier League successes of 2011 and 2012.
Injuries cost him a regular place during the 2012/13 season and, after spending the past year on loan at Fiorentina, he is now ready to move on.
Richards wrote on Instagram: "I just wanted to thank the Man City fans for the amazing support they've given me over the years.
"I joined City when I was 14 and have been part of a brilliant period in the club's history - winning our first league title in 44 years, winning the FA Cup, playing in the Champions League.
"The club, the manager, the staff who work behind the scenes, the players, but most importantly the fans - everyone - will always have a special place in my heart.
"City's been like a family to me and I wish everyone the best of luck for next season and the coming years."
Source : PA
Source: PA