Both Tony Mowbray and Michael Beale were sacked by the Black Cats this term.
Per The Mirror, Defoe said: The Sunderland job? Why not?
Even when I was a player, I always used to say I'd love to manage this club. If I got an opportunity, I wouldn't shy away from it, so let's go."
Defoe added: I spoke to Antonio Conte when he was at Tottenham last season about his journey into the game.
I spoke with Gareth Southgate for two or three hours about Middlesbrough, at 35, going from being captain to all of a sudden getting a call in the summer asking him to become manager. Everyone's journey is different. The most important thing is knowing who you'll take with you and I've got that.
Paul Bracewell and me, we are so close. He's experienced, a great player. I'm getting all these gems from experienced coaches. You have to be obsessed with the game, I say that to young players all the time. A lot of young players don't watch football now, that blows my mind.
"I don't know if other players are like that, if other players have a relationship with fans and a club and think they'd love to manage this club. I always believe I will get an opportunity. I was never a person to say: 'hmm, I don't know'.
"As a player I'd go and stand with the first team, next to Rio and Frank and say I'm not going over there! I want to be with the first team! You have to have that confidence. I have put in hard work, played for 23 years. Two years learning at Tottenham."