The 26-year-old has been at White Hart Lane since joining from Derby County in 2005, but will now discuss personal terms with the Black Cats.
However, the London Evening Standard reports that England international may have to take a £5,000 cut in his £40,000-per-week wages.
Fulham have also been credited with an interest in Huddlestone, who will undergo a medical in the North-East ahead of a potential move.
Paolo Di Canio has been busy in his first transfer window in charge of Sunderland, securing the signatures of El-Hadji Ba, Jozy Altidore, Vito Mannone, David Moberg Karlsson, Modibo Diakite, Cabral and Valentin Roberge.
Meanwhile, talks with Juventus midfielder Emanuele Giaccherini are ongoing.