The 13-time England international looks set to leave the Etihad Stadium in a cut-price deal in the coming weeks, with the Sky Blues having failed to agree a new contract with him.
Richards has just one year to run on his deal, and was seeking assurances regarding his first-team opportunities before committing to his boyhood club.
But Manuel Pellegrini was unwilling to offer him the minutes he craved, which has now opened the door for a knockdown move, with City keen to get some cash for their man.
Newcastle have been alerted by this and are ready to launch an official bid as they plot for the loss of Mathieu Debuchy.
The Magpies’ right-back is said to be in talks with Arsenal, which are likely to result in him moving to north London for around £12m.
Alan Pardew sees Richards as a good replacement, with the powerful 26-year-old able to play on the right side of the backline, or in a central defensive role.
Liverpool have also been linked with him, but the Tynesiders are hopeful that a greater chance of being a guaranteed starter at St James’ Park may give them an advantage over the Reds.