Blues were relegated from the Premier League during the 2005-06 season with Bruce in charge, but he led them back to the top flight the following campaign.
Savage, who now works as a BBC pundit, played under Bruce at St Andrew’s.
“It all boils down to results and his performances for Birmingham against Villa in the derbies. When we were in the Premier League, we absolutely battered them time after time,” Savage added.
“I think Villa fans will remember that. They had better players than us but we had this team spirit, this togetherness and we battered them more times than not in massive pressure games so I think Bruce will be the right man.”
Former England defender Danny Mills told the Monday Night Club on BBC Radio 5 live that the Championship side had to get the “best man for the job”.
“I don’t understand this fixation that he was Birmingham manager so he can’t do a good job for Aston Villa,” Mills said.
“It makes no sense. Surely if he goes there and does a good job, fans have got to come around to that way of thinking.
“It’s not like he was born and bred at Birmingham, played there his whole life. He’s managed other clubs.”
In 2011, Villa appointed Alex McLeish, who had resigned as Birmingham boss days earlier, but he was sacked 11 months later.