The England international has a clause in his contract that allows him to leave the Stadium of Light if the club suffer relegation from the Premier League.
After dropping into the Championship last season, it has been widely expected that Defoe will move on, and it seemed as though a switch to the south coast was on the cards.
However, according to the Daily Star, Bournemouth are wary about paying too much for a player who will turn 35 in October.
The report claims that Defoe, who scored 15 league goals for Sunderland last season, is angling for £80,000-a-week wages on a three-year deal, and also wants an £8m signing-on fee.
West Ham United have also shown interest in the striker.