The club sacked the Italian on Sunday - but no appointment will be made before the weekend, with Kevin Ball taking charge of the next two games, including the Capital One Cup tie against Peterborough.
Sky Sports News reporter Keith Downie said: "There are eight or nine names on the list and Gianfranco Zola and Gus Poyet are two names high up on the list."
Gus Poyet, the former Brighton manager, is Sky Bet's current odds-on favourite to fill the vacancy, with Roberto Di Matteo and Steve McClaren next on the list.
Watford manager Gianfranco Zola says he is happy to be named among the contenders to succeed Di Canio, but he is also focused on his job at Vicarage Road.
The Italian told Sky Sports News: "Of course I am flattered that I have been considered but I am really happy over here and like what I am doing.
"I think my growth as a manager has been massive and so I want to fulfil this task that I will be here."
Celtic boss Neil Lennon is another man reportedly in the frame, but he has distanced himself from the job by insisting he has no intention of leaving Parkhead.
"I'm not aware of me being linked with anything. You are asking the wrong person," he said.
"Maybe you should ask the people linking me with the jobs. I'm not aware of who they are. I'm very, very happy doing what I'm doing at the minute."
Di Canio was axed after some senior Sunderland players complained to the club about him, Sky sources understand.
In the fallout from that meeting, some of the club's senior men went above Di Canio's head to express their concerns about his management style.
In his six months on Wearside Di Canio increased the workload in training and was at times publicly critical of his players but - this season, at least - his methods have not paid off.
Ball - a player on Wearside for almost all of the 1990s - will reprise a role he previously held for 10 games following Mick McCarthy's 2006 departure.
He said: "The situation last time was slightly different to this time, but it did give you an experience, whether it be for one or 10 games.
"I enjoyed it last time and I hope I feel the same way about this one as well. It allows you to say, 'Well, I have done it before, it's not something that's unexpected'.
"I have coached for 10 years, so within that, you do so many things that a manager would do anyhow, it's not a fantastically, unbelievable step."