The 25-year-old cost Villa £8m from West Bromwich Albion in 2008 after a season-long loan spell at Villa Park.
The Potters may have to sell before bringing any players in, with former skipper Abdoulaye Faye among those who could leave the club in January.
Davies, who started his career at Luton Town, has not started a Premier League game since August 2009.
An ongoing shoulder problem, combined with the additions of defenders Richard Dunne and James Collins last season, has restricted Davies to just 227 minutes of football in cup competitions before his loan move to the Walkers Stadium, during which time he has started 12 matches.
Stoke manager Tony Pulis has already confirmed that he is not interested in a move for Villa's unsettled midfielder Stephen Ireland during the January transfer window.
Source: BBC Sport
Source: BBC Sport