The Premier League pair have been linked with the powerful enforcer for some time, but have seen their desire to land him thwarted by the Sky Blues’ eagerness to keep their man.
However, their stance is said to have altered in recent times.
City rejected a loan offer from Liverpool for Richards on deadline day during the last transfer window, but it is believed that he has little future at the club beyond the summer.
A series of injury woes have seen him lose his right-back role to Pablo Zabaleta, while a place at the heart of the defence – which has long been regarded as his preferred position – seems even more unlikely given Manuel Pellegrini’s options.
Arsenal could move to offer him an escape route when the next window opens, with both clubs keen to offer him regular action.
Richards was believed to have ambitions of making England’s squad for the World Cup, but a trip to Brazil looks unlikely unless he feature regularly between now and the end of the season.