Smith is keen to add a solid right-back to his ranks, and Villa are considering making a bid for the 27-year-old former Newcastle United right-back.
The report claims that Championship outfit West Bromwich Albion and Premier League club Brighton are also in the hunt for his signature.
Tavernier has been superb for the Gers since he joined the Ibrox club in 2015. The Gers skipper is a key player for Steven Gerrard’s side, and the Ibrox club will be looking to hold on to him.
Last season, he managed 17 goals and 20 assists in all competitions, and his performance at Rangers suggests that he would be good enough to play at the highest level.