Sky Sports understands that Richards confirmed to City chiefs in early March that he would not be signing a deal which was offered to him last summer.
Richards, who has come through the ranks at City, has decided that the time is right to seek a new challenge.
The 25-year-old has just over 12 months left on his current deal at the Etihad Stadium and City were keen on extending his stay to keep him at the club.
However, with first-team football not guaranteed under Manuel Pellegrini, Richards is now looking elsewhere and City will opt to sell this summer rather than risk losing him for nothing in a year's time.
A source told Sky Sports: "It is with a heavy heart that Micah has told City that he will not be signing his new deal and they have now accepted he will be leaving. Micah has grown up at City and given his all but this is the right time to move on."
A host of clubs are now monitoring Richards, who has spent much of his time at City at full-back, but is also viewed as a centre-half.
In the Premier League, Arsenal, Liverpool, Newcastle, West Ham and Tottenham are all believed to be monitoring the situation, whilst there are clubs in France, Spain and Italy also looking, with AC Milan known to be one of those keen on taking him.
A spokesman for Richards' agents Sidekick refused to comment on the situation.