It is thought the former Birmingham and Hull manager is now considered the leading contender for the position along with current caretaker boss Steve Clarke.
Another favourite for the job, David Wagner, appears to be out of the reckoning after his chairman at Huddersfield, Dean Hoyle, suggested he would not be leaving the West Yorkshire club.
Villa are looking for a new manager after sacking Roberto Di Matteo earlier this week, just 12 games into his reign, following a poor start to the season. Villa, relegated from the Premier League last season, are currently 19th in the Sky Bet Championship.
No interviews for the position have yet taken place but Bruce, who spent almost six years at rivals Birmingham and has been out of work since leaving Hull in July, is firmly on the radar. He is also understood to want the job.
Clarke, the former West Brom boss who joined the coaching staff in the summer, is also thought to be in contention with the club impressed at how players have responded to him this week.
The pair look to be the chief contenders for the post with Brentford’s Dean Smith also seemingly out of the running.
The highly-regarded Wagner, who has guided Huddersfield to the top of the Championship, appears keen to stay at the John Smith’s Stadium.
Hoyle said: “David has told me that he would never leave us for another Championship club, regardless of which club that is.”