The powerful defender looks set to leave the Premier League champions in the coming months amid talk that he has opted against extending his contract, which expires in 12 months’ time.
Despite City having shown a willingness to keep their academy graduate as they look to meet home grown player rules in their squad, Richards is thought to see his career at a crossroads, with a series of injuries over the course of the past few years having prevented him from living up to his full potential.
The 25-year-old is believed to be desperate to be a first-team regular, which has alerted the Hammers.
Sam Allardyce sees the versatile enforcer – who can play at right-back or in the centre of the backline – as a wise addition, and is willing to offer him guarantees in regards to playing time as he plots to bring a more attractive playing style to east London.
Despite City being aware that they could lose their man for free next year they are asking for around £5m, which could be a stumbling block for the Irons when combined with his £70,000-per-week salary.