The Reds currently have no fewer than five senior defenders on the side-lines with Mamadou Sakho, Glen Johnson, Sebastian Coates, Daniel Agger and Jose Enrique all nursing injuries.
However, they will not be helped out by the Premier League leaders, who are keen to keep hold of the England international.
Richards’ opportunities at City have been limited in recent seasons, though he spent most of the 2012/13 campaign on the treatment table.
He has made two league appearances since Manuel Pellegrini arrived at the Etihad Stadium, while he has turned out the same number of times in both domestic cups, and three times in the Champions League.
The Birmingham-born defender has spent his entire career so far with the Sky Blues, winning the FA Cup and Premier League during his nine years with the first team.