Apparently Mike Ashley is willing to smash his wage cap and match the 25-year-old's £70,000-a-week wage.
Richards, who has made just 18 appearances in the last 18 months due to knee and hamstring injuries, has a year remaining on his current contract with City and stalled discussions over a new deal on similar terms last summer.
Having fallen firmly behind Pablo Zabaleta as Manuel Pellegrini's first-choice right-back, Richards is keen to become a regular in the Premier League.