The 24-year-old has been sidelined since October, and as a result has fallen down the first-team pecking order at the Etihad Stadium, with Pablo Zabaleta currently enjoying an impressive season on the right side of defence.
Richards needs regular football if he is to get back into the international reckoning, with one eye on making Roy Hodgson's England squad for the World Cup in 2014.
His continued absence from Roberto Mancini's starting XI could prompt a summer move for the full-back, with Arsenal ready to offer the player an escape-route.
Gunners boss Arsene Wenger is on the lookout for a replacement for Bacary Sagna, who is expected to leave the Emirates Stadium at the end of the season.
The north Londoners do have another of England's most promising youngsters in the form of Carl Jenkinson already on their books.
However, Richards's ability to play at central defence as well as on the right, is an attractive proposition for Wenger, who is ready to move for the Manchester City star when the transfer window reopens on July 1.