The Daily Star claims that the Magpies are keen on the 25-year-old defender, whose progress at the Etihad Stadium has been hampered by injuries in recent years.
It has been reported that Newcastle will be able to pay him his current wage of £72,000 a week, and that manager Alan Pardew will guarantee him a certain number of games.
Richards has featured in 10 matches in all competitions for Man City so far this season and is said to be desperate to play more games.
The England international, whose current contract with City runs out in June 2015, is rated at £8m.
Richards has been at City his entire professional career.