Borussia Dortmund have made their first signing after Jurgen Klopp's departure by landing midfielder Gonzalo Castro.
Di Canio is set to hold talks with Sunderland officials with a view to being formally appointed on Monday.
Di Canio's immediate objective will be to revitalise a squad for a seven-game run-in which will determine where the Black Cats will play their football next season.
They are currently just a point above the Barclays Premier League relegation zone after a run of eight games without a win.
It appears club owner Ellis Short is determined to make an appointment sooner rather than later ahead of a difficult run of games which takes the Black Cats to Chelsea next weekend ahead of a derby trip to Newcastle and the visit of Everton, whose 2-0 FA Cup quarter-final replay victory on Wearside last season had such devastating consequences for O'Neill's reign.
The new man will be Sunderland's fifth manager in a little more than four years, and the first the American will have chosen since Niall Quinn's departure as chairman.
Di Canio's appointment would undoubtedly represent a gamble for Sunderland given his volatile nature.
The 44-year-old resigned from his post at Swindon in February, citing a number of off-field events including the sale of star man Matt Ritchie.
Di Canio joined the Robins in May 2011 and departed with the club top of the Ligue 1 table having overseen their promotion from League Two.
After leaving Swindon he outlined his belief that he was now ready to manage at a higher level, telling BBC Sport: "I believe I am at a stage now where I am a Premier League or Championship manager.
"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.
"You can imagine if I had the chance to do the same at the top level.
"I proved in League One and Two that I was the best manager, and I now feel ready for the next level."
If he does land the job, Di Canio faces the task of galvanising a dispirited squad for a task in which they cannot afford to fail, with the financial implications of the new broadcasting deal meaning relegation is simply not an option.
Sunderland have at times been abject during a run which has seen them collect just three points from the last 24 on offer, and their lack of goals - they have scored just seven and conceded 12 in the process - has been brought into sharper focus by the loss of leading scoring Steven Fletcher through injury for the remainder of the campaign.
Skipper John O'Shea acknowledges that is a situation which cannot be allowed to continue if they are to escape the drop, and he insists January signing Danny Graham cannot bear that burden alone.
He said: "Look, it's so blatantly in front of us. Everyone just has to take responsibility, whether it's scoring from set-pieces, midfielders having shots, scoring goals.
"From last season, it's been a poor return from everyone in that sense, and that's something we will have to work on.
"You need that bit of quality to score goals and create chances, and that's something we are going to have to keep working on and keep believing that we can do it.
"It's going to have to happen at some point because obviously we are missing Fletch, who has been fantastic for us.
"It was hard for Danny in that lone role up top working his socks off. We need to get more support for him and better quality."
Meanwhile, Liverpool boss Brendan Rodgers and Aston Villa counterpart Paul Lambert have slammed Sunderland's decision to sack O'Neill.
Rodgers, whose side defeated Lambert's men 2-1 at Villa Park today, said: "I was very surprised. Whenever someone of the status of Martin O'Neill loses his job, then we all have to be on the back foot.
"This is a guy who has been in the game for many years, has many years experience, went into Sunderland and picked them up off their knees.
"Okay, they are going through a difficult time, but he is still a top-class manager.
"I hear the same things about Stoke and Tony Pulis. I think some clubs need to be careful. They need to understand where they are at.
"They won't always be on the front foot going forward.
"I think if you ask clubs like Leeds, Portsmouth and Barnsley, teams that were in the Premier League, they would be happy with people like Martin O'Neill and Tony Pulis and guys like this.
"There are some times when the club just has to be stable and guys like Martin O'Neill losing his job, it's a sad day."
Lambert played under O'Neill at Celtic and still refers to him as 'the gaffer'.
He said: "I only knew late last night and I was shocked like everybody else at what had happened. I was shocked.
"Nobody is safe. I had the privilege of working under him for five years and it was fantastic.
"If you make that change....I'm not so sure...you'd think someone is going to appointed pretty quickly there at this stage of the season."