The England star looks set to leave the Etihad Stadium in the summer after an injury-ravaged few seasons, with the player keen to play regularly in a bid to get his career back on track.
Liverpool attempted to snap up the powerful and versatile enforcer on loan in January, but saw their efforts thwarted by Manuel Pellegrini’s reluctance to let his man go.
Richards will enter the final year of his contract soon, but City will demand around £8m from their title rivals for the 25-year-old.
Despite his fitness worries, Rodgers is desperate to add the right-back/centre-back to his ranks as he seeks to build a squad capable of challenging for domestic and Champions League honours next term on the back of an impressive 2013/14.
The Northern Irishman also has a good record of getting the best out of players who were on the fringes of other big clubs’ squads, with Daniel Sturridge and Philippe Coutinho having thrived at Anfield since arriving from Chelsea and Inter Milan respectively.