The Wearside club are looking for a new manager after parting company previous incumbent Paolo Di Canio, who led them to just one point from their opening five Premier League games.
Uruguayan Poyet has emerged as a leading contender for the vacant position, with the likes of Roberto Di Matteo and Steve McClaren also thought to be among the front runners.
And Poyet - who was relieved of his position at Brighton in June - has now announced his intention to be the new man in charge at the Stadium of Light.
Speaking to the Daily Mirror, he said: "My opportunity to manage Sunderland is there. I'm waiting. Nervously.
"Since the start of the season, I've dedicated myself to watching the games of teams that might call me if things weren't going well."
Caretaker manager Kevin Ball is also thought to keen on the post, and he guided Sunderland to a 2-0 League Cup victory over Peterborough United on Tuesday.
Ball is also set to be in the dugout for their home Premier League fixture with Liverpool on Sunday.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
