Richards is set to leave the Etihad Stadium at the end of the season after falling out of favour under Manuel Pellegrini.
The 25-year-old has featured in just 10 games so far this season as he hasn't been able to dislodge Pablo Zabaleta at right-back.
Richards, who has struggled with injury this season, can also play at centre-back but has again been overlooked despite the fact Manchester City have struggled in that area of the pitch.
Reports suggest Richards has been offered a new deal to stay at Manchester City - but has rejected the chance to extend his stay at the Citizens.
Arsenal are also said to be in the running to sign Richards as they are currently scouring the transfer market for a potential replacement for Bacary Sagna.
The Gunners' interest could see the north London side go head-to-head in the running to sign Richards - along with north-east giants Newcastle.
SkyBet odds on where Richards will be playing next season:
Liverpool - 3/1
Newcastle - 6/1
Arsenal - 8/1
West Ham - 9/1
Leicester - 16/1