Tudor's position is already in serious doubt after four defeats in his first games in charge.
With Spurs just one point above the dropzone, the board is considering axing Tudor and bringing in a survival specialist for the remainder of the season.
Former Tottenham midfielder Poyet is currently a free agent after a successful one-year stint at K-League outfit Jeonbuk Hyundai Motors which ended in December.
Poyet told The Sun for Gambling.com: “With respect to Igor, yes – for sure. I mean, I know everything. Sometimes they don’t put me in that position.
“But you know, I remember before Igor Tudor got the job, people were talking about Robbie Keane – rightly so. They were talking about Tim Sherwood – rightly so. Even Harry Redknapp, they were asking him.
“And I was sitting at home and I’m thinking, ‘Why not me?’ I’ve been there. I know the place, I know the relegation battle.
“I know what needs to be done. Well, at least I have the experience. I know the Premier League. It’s sometimes funny that your name is not related there, but that’s the way it is now.
“You need to put yourself in the press. If they think it’s me I would be more than happy but it wasn’t me. And now the only thing that I want as a coach is for Igor Tudor to sort it out for him, as a coach.
“To have that feeling that he sorted it out and Tottenham stay up. Nothing else.”