The 24-year-old endured an injury-ravaged campaign last season, with ankle and then knee troubles restricting him to eight appearances.
But the signs are that Richards is very much part of the plans for new boss Manuel Pellegrini, and City's hierarchy, including director of football Txiki Begiristain, are ready to talk terms.
Sky Sports understands that Richards's representatives are due to meet the club this week and the prospects are that the England defender will commit his long-term future to the club.
A number of clubs from the Premier League and the continent had been keeping tabs on Richards's situation but, subject to terms being agreed, he seems set to remain with the club he has spent his whole career with.
Richards has two years left on his current deal, which he signed in 2011.