The Manchester City defender, who is on a season-long loan at Fiorentina, is also a reported target for Liverpool, Newcastle and West Ham ahead of his contract expiring this summer.
The Manchester City defender, 26, joined Fiorentina on a season-long loan in September but has had to settle for a backup role since, making 19 total appearances – seven of them coming in Europa League action.
Out of contract this summer, the former England international is now expected to return from Serie A to find another Premier League suitor, with Villa named as one of his potential destinations.
Manager Tim Sherwood is said to have made his interest in the Birmingham-born right-back known in the past fortnight, as he prepares to remodel the squad former boss Paul Lambert left him in his first transfer window in charge of the club.
A regular role at full-back would be far from guaranteed were he to arrive at Villa Park in the coming months, with Alan Hutton and utility man Leandro Bacuna both providing strong competition, but his ability to play in central defence could see him become a valuable squad member.
Furthermore, while he has not featured in the English top-flight since November 2013, the City product's age and experience would certainly suggest that he would be a more than welcome addition on a free transfer.
However, with several Premier League rivals said to be keen on Richards as well, bringing him to Villa might not prove such a straightforward task for Sherwood.