The man asked to take temporary charge of the Black Cats in the wake of the Italian's departure on Sunday night guided them to a 2-0 Capital One Cup third round victory over League One Peterborough, and then revealed he would like the job on a full-time basis.
Goals from Emanuele Giaccherini and Valentin Roberge were enough to see Sunderland through to the next stage as they dominated on a wet Wearside Tuesday evening.
In the aftermath of the victory, who also had a spell as caretaker in 2006, staked his claim to become the new Sunderland manager.
"Anybody who is anybody would like to be considered for it," he said. "In the sense of what I have done as a coach or a player and not only that, my qualifications I have gone out and got as a coach, I would like to be considered.
"But ultimately, that's the club's decision and I would go with that, whether it was me or someone else, they would have my full support."
Owner Ellis Short is understood to have drawn up a shortlist of potential successors to Di Canio, with former Brighton manager Gus Poyet having replaced Roberto Di Matteo at the head of the bookmakers' field.
However, the players Ball inherited from Di Canio could not have done a great deal more to further his application with a confident display against Darren Ferguson's men at the Stadium of Light.
Summer signing Giaccherini, who had been substituted at half-time in Saturday's 3-0 Premier League defeat at West Brom, fired the Black Cats into a deserved 32nd-minute lead from Lee Cattermole's cross.
"I thought Cattermole put in an excellent performance, along with a lot of others as well," the interim manager said.
"I just thought it was a really good performance in the sense that they worked very hard, but also played some good football and created a lot of chances as well.
"We also have to give credit to Peterborough because they came up with a decent game-plan - you can see why they are doing very well at the moment and we wish them all the best as well."
Peterborough boss Ferguson was disappointed with his side's display, which allowed Sunderland to establish momentum in the tie.
"We spoke about certain things Sunderland might do and their strengths and what we felt might be weaknesses, but I have got to make sure my teams plays to a level we know we can and in the first half, we didn't, it's as simple as that," he said.
"We were in the game. We felt the longer it went at 1-0, perhaps we had more of a chance because we know it can get quite frustrating for the fans here. That's evident, especially at the moment.
"But to lose two goals from two crosses is poor, we shouldn't be losing goals like that."