The right-back has been offered a new five-year deal, but he has told City chiefs he is unwilling, as it stands, to put pen to paper.
His existing deal expires at the end of the next season, but the Etihad Stadium club would rather sell Richards in the summer than lose him on a free transfer in 2015.
The defender has only featured in two Premier League games this season and neither of them were in 2014.
His only outings this calendar year so far have been in FA Cup victories over Blackburn and Watford.
Richards was a loan target for Liverpool in January.