The former Brighton boss was always considered one of the favourites to replace Paolo di Canio in the Wearside hotseat.
Di Canio was sacked on Sunday night, the day after their 3-0 defeat to West Brom which left them bottom of the Premier League with one point from their opening five games.
It later emerged that senior Black Cats players had complained to the club's hierarchy about the fiery Italian's behaviour.
Kevin Ball has been appointed as caretaker manager and he guided Sunderland to a 2-0 win over Peterborough in the Capital One Cup third round on Tuesday night.
Ball has stated that wants the job on a permanent basis, and he will take charge of the team again this weekend when they face Liverpool.
Ball told Sky Sports News: "Anybody who is anybody would like to be considered for it.
"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."
Sunderland owner Ellis Short has insisted he will not rush the appointment, having sacked Di Canio after just 175 days and 13 matches in charge.
Former Sunderland striker Kevin Phillips told Sky Sports how Di Canio's sacking was no surprise because the players hold the power now.
The veteran Crystal Palace forward said: "Speaking as a player that's played under many managers over the years, once you lose that dressing room you lose your players - they don't trust you.
"I think the chairman and the board had no choice but to relieve Paolo of his job and duties, because in this day and age I believe that man management is more important than actual tactics on the pitch and I think there wasn't any of the at the Stadium of Light.
"Once you lose that dressing room you're on a hiding to nothing. I would certainly say that with the regime he was running there, allegedly.
"If you believe everything you read - banning smiling, staff aren't allowed to talk to players, no tomato ketchup, no coffee - I don't believe you can do that in this day and age.
"You're talking about fully-grown men that have got their own families - you can't treat them like kids. You have to treat them like adults and I believe Di Canio's style doesn't work for me in the Premier League."