Sky Sports understands the Italian, who left his role with Swindon last month, is close to signing a two-year contract with Sunderland.
Sunderland chairman Ellis Short said earlier on Sunday that he was keen to make a quick appointment after taking the tough decision to let O'Neill leave in the wake of the 1-0 defeat by Manchester United.
That defeat left the Black Cats precariously positioned one point outside the bottom three in the Premier League table with seven games left in the season and time running out to turn their form around.
Di Canio was among the early favourites to take over, along with Roberto Di Matteo and Steve McClaren, but the support increased for him on Sunday morning with punters snapping up every price all the way down to odds-on in Sky Bet's Manager Specials.
He had recently been linked with the vacancy at Reading after leaving Swindon towards the end of February, in the wake of a row over the club selling winger Matt Ritchie to one of their main rivals in League One, Bournemouth, behind his back.
He recently stated he was ready to make the step up to the Premier League, saying on his BBC blog: "I have already proven my ability in League Two and League One, where there are many arrogant and average players and I was able to turn their mentality and help them become better footballers.
"My plan for now is only to watch the top level of football - Premier League and Championship - because the next step for me is important.
"I will be watching games in the Premier League and Championship because this is my future, obviously, and I hope one day I can be there.
"The right place for me is the place that has the ambition and the staff who want to bring in a winning mentality.
"The club needs to have set rules, which for me are discipline, desire, passion, work ethic and a determination to get the right results to make everybody happy, namely the board, the fans and the club's players and staff.
"I believe I am at a stage now where I am a Premier League or Championship manager."