The former Manchester City right-back, who spent last season on loan with Serie A club Fiorentina, is a free agent after leaving the Etihad Stadium.
It is understood Villa have offered the 26-year-old an opportunity to revive his career in the Barclays Premier League.
Richards - a 13-time England international - won two league titles, the FA Cup and the League Cup with City but last featured for Manuel Pellegrini's side in a home defeat to Wigan in March 2014.
Losing FA Cup finalists Villa, now managed by Tim Sherwood, are keen to bolster their defensive options after conceding 57 league goals during the 2014-15 season - a campaign which saw them escape relegation by only three points.
Source : PA
Source: PA