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."

Ex-BBC journalist Jacky Sutton, 50, was found dead in a toilet at the city's Ataturk airport between 17-18 October.
She was the acting Iraq director for the Institute for War and Peace Reporting (IWPR) and was travelling from London to Irbil, northern Iraq.
In a statement Jenny Sutton, Ms Sutton's sister, said "at this stage we believe that Jacky acted alone".
But the statement added that there remained "the possibility that additional information will come to light".
An investigation into the death is currently being carried out by Turkish authorities.
The statement said the family and the IWPR had carried out an "extensive review" of information provided by Turkish authorities.
Jenny Sutton said: "The family is satisfied with the investigation undertaken by the Turkish authorities.
"We were deeply sceptical about initial reports. But based on the evidence we have seen, at this stage we believe that Jacky acted alone."
The family and the IWPR said the Turkish authorities had provided access to "the complete dossier of evidence" relating to the case, including copies of CCTV images from the airport and witness statements.
This all indicated that Ms Sutton had been alone and there was no evidence of a struggle, they said.
The decision to release information from the investigation had followed "widespread speculation" about the circumstances surrounding Ms Sutton's death, the statement added.
The IWPR and the family said they would seek a further assessment from an independent investigative expert to confirm the findings once the Turkish investigation was complete.
The London-based IWPR supports local journalism in countries affected by conflict and crisis.
Its previous Iraq director, Ammar Al Shahbander, was killed in a car bomb attack in Baghdad on 2 May and a memorial service had been held for him in London last week, according to the IWPR website. Ms Sutton had been in London attending the service.
Ms Sutton worked for the BBC World Service between 1998 and 2000, reporting from Africa, the Middle East and London.
She also served in senior roles at the United Nations.
The IWPR described Ms Sutton as "extremely bright" and "universally loved".
Former Birmingham City boss Steve Bruce is the "right man" to manage Aston Villa, according to former Blues midfielder Robbie Savage.
[NEXT_CONCEPT]
No other parties were involved in the death of a British woman at an Istanbul airport, her family believes.