The 70-year-old was dismissed by Birmingham City in September after just eight league games of the Championship season, during which time the Blues had amassed just four points.
The Black Cats have endured a torrid time back in the second tier, meanwhile, and decided to part ways with Simon Grayson on Tuesday after registering just one win in their first 15 games.
Redknapp has been installed by the bookies as one of the contenders to take over at the Stadium of Light in the wake of Grayson's sacking, but the former Portsmouth, Tottenham Hotspur and West Ham United manager says that he has not yet been contacted about the role.
"It's the first I've heard of it," he told talkSPORT. "I've never spoken to anybody.
"I am getting bored though, I must admit. Sandra is getting more bored of me, more importantly!
"Sunderland is a great club with great tradition. It shouldn't be where it is at the moment. It is another club that should be doing a lot better."