The former England international looks set to leave the Etihad Stadium this summer after rejecting a new contract, with his current deal due to expire in 12 months’ time.
City offered the 26-year-old fresh terms, but with guarantees surrounding game time not forthcoming, he opted against putting pen to paper.
This has alerted Liverpool, who are ready to pay the Sky Blues – who beat them to the title last season – a minimal fee for the defender.
Richards has endured an injury ravaged few years, but is understood to be nearing full fitness and is seeking game time to fulfil his once burgeoning reputation.
City may accept offers of around £5m for their man rather than risk losing him for free next year.
Arsenal, Newcastle and West Ham have also been linked with the 23-time England star, but Rodgers’ personal desire to get the burly enforcer to Anfield could well be a deciding factor.