The 48-year-old, who also also took charge of the Black Cats for 10 games in 2006 following the dismissal of Mick McCarthy, was in the dugout for Tuesday's 2-0 win over Peterborough United in the Capital One Cup.
|16/1||Kevin Ball is 16/1 with Coral to be appointed Sunderland boss
"Anybody who is anybody would like to be considered for it," he told reporters.
"In the sense of what I have done as a coach or a player and, not only that, the qualifications I have 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."
Emanuele Giaccherini and Valentin Roberge notched against the League One side as Sunderland booked their place in the fourth round of the Capital One Cup, and Ball praised the team's performance in light of the uncertainty around the club.
"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," he said of the win.
"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."