The former Watford manager has impressed many in the game with his Clarets side this season.
The Clarets slipped back into the Championship this season after promotion the year before, but their boss has been roundly praised for his management in keeping Burnley competitive on a tight budget.
Sunderland themselves only escaped relegation in the last couple of games of the campaign, finishing just five points above Dyche's Burnley side, but they have seen the man that presided over their route to safety leave since the season's end, as Dick Advocaat retired from football management all together.
It has meant Ellis Short and his board are looking for yet another boss, with no manager completing a full season in charge of the club since Steve Bruce in 2010.
43-year-old Dyche took Burnley up last season as Championship Runners-up, having started his management career at former club Watford, but ahead of increased bets on him taking over at the Stadium of Light, Sky have revealed that no talks have taken place about a switch.
Fans of the Lancashire club will be desperate for him to stay, but with Sunderland able to offer Premier League management, Dyche will remain one of the favourites for the vacancy unless he comes out and denies interest in the position.