The former England international is currently in his second season with Serie A giants Roma, but has fallen out of favour under manager Rudi Garcia.
Paris Saint-Germain loanee Lucas Digne has been Roma’s first-choice left-back this season, and Cole is yet to feature in a match-day squad after refusing to cancel his contract during the summer.
However, the Daily Star claims that Cole will leave the Italian side as a free agent in January and is consequently on the look-out for a new club.
A return to England and the Premier League is said to be Cole’s preferred option, and a move to Villa could be on the cards following an injury to Jordan Amavi.
Remi Garde’s side look set for a relegation scrap after collecting just six points from 15 games, and are currently bottom of the league as a result.
The former Lyon boss is desperate to make signings next month and apparently sees Cole as an ideal replacement for Amavi.