Sunderland sacked Bruce on Wednesday after club chairman Ellis Short said results were "simply not good enough".
The north-east club's 2-1 home defeat by fellow strugglers Wigan on Saturday left Sunderland 16th in the English Premier League and just two points above the relegation zone.
Bookmakers have tipped Mark Hughes, who left Fulham in June, as the man most likely to succeed Bruce however while O'Neill is also a hot favourite the Irishman is said to be the popular choice to take over at the Stadium of Light.
O'Neill has been out of the game since leaving Villa in acrimonious circumstances in August last year, but has been linked with virtually every managerial vacancy since.
He has vast experience after launching his career with Wycombe, and his spells at Norwich and Leicester won him a chance to manage Celtic before heading south of the border once again.
Oversees candidates Carlos Queiroz and Ronald Koeman have also been linked with the job, although Sunderland are understood to want a man with Premier League experience.
They are also keen to avoid a compensation battle, so suggestions that Everton's David Moyes could be a serious contender seem wide of the mark.
Former Manchester United defender Bruce joined the Black Cats from Wigan before the 2009/10 season and struggled to win the affection of some Sunderland fans who resented his boyhood support of local rivals Newcastle United.
But, despite some of the taunts aimed at Bruce at the weekend by angry fans at the Stadium of Light, Dallas-based businessman Short said his was not a knee-jerk decision.
"This has been a difficult time for everyone at Sunderland and is not a situation that any of us envisaged or expected to be in," said Short in a statement released on Sunderland's official website.
"It is my job as chairman to act in the best interests of our football club at all times and I can assure everyone that this is not a decision I have taken lightly."
Bruce's assistant Eric Black will take charge of the side for Sunday's trip to Wolves.
Source: AFP
Source: AFP