Bruce, without a club since leaving Hull in July, is favourite to replace Roberto di Matteo, who was sacked by the Championship club on Monday.
Savage said Bruce has experience in the division and still lives in the area.
"He took Birmingham up, he took Hull up," said the Welshman. "He won't have to travel, he won't have to uproot."
Blues were relegated from the Premier League at the end of the 2005-06 season.
But Bruce, who had been in charge of Blues since 2001, led them back to the top flight the following season - and also went on to win promotion to the Premier League with Hull twice too.
Savage played under Bruce at St Andrew's and thinks Villa fans will not worry too much that Bruce used to manage their city rivals.
He also says Bruce's ability to get the best out of the Birmingham players whenever they played Villa will count for a lot.
"When we were in the Premier League, we absolutely battered them time after time," said Savage. "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."
Villa have appointed a former Birmingham boss as manager in the past - and the outcome was not good.
Alex McLeish lasted just 11 months before he was sacked in May 2012.
During his reign, the Scot was often targeted by Villa supporters angry that the club had who appointed a former Blues manager as their boss.
Former England defender Danny Mills told the Monday Night Club on BBC Radio 5 live that Villa had to get the "best man for the job" and thinks Bruce could be a good option despite his association with Birmingham.
"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."
Former Birmingham City boss Steve Bruce is the "right man" to manage Aston Villa, according to former Blues midfielder Robbie Savage.