The Black Cats have been aligned with the Belgium international of late amid suggestions that Dick Advocaat is eager to add the former Fulham man’s energetic and powerful presence to his midfield ranks.
However, even though the 28-year-old endured a difficult 2014/15 season at White Hart Lane the London club want £15m for his signature.
Such a sum would match the figure they paid for Dembele three years ago, and White Hart Lane chairman Daniel Levy is known for his strong negotiation style.
The rangy star started for Spurs during their Premier League-opening game at Manchester United, hinting that he has a future at the club under Mauricio Pochettino.
Dembele made his name in Dutch football with Willem II and AZ Alkmaar before joining Fulham in 2012.