The former Birmingham and Hull manager has held initial discussions with Villa and is now considered the leading contender for the position along with current caretaker boss Steve Clarke.
"I've had a chat with them
That's as far as it's gone," Bruce told Sky Sports' Goals on Sunday programme.
"They did say they're in a process, which you have to respect
I'm hoping that I hear something this week
It would be a terrific job
"I'm sure everybody would agree that it's one of the big clubs of this country.
"It needs a little bit of turning round at the moment, but they've got a huge support and it's a big, big club.
"Let's hope I hear something."
Bruce spent almost six years at Villa's city rivals Birmingham and has been out of work since leaving Hull in July.
Villa, who play Wolves on Saturday, are looking for a new manager after sacking Roberto Di Matteo, 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.
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.
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.
Source : PA