The Black Cats have made an enquiry to Fulham over the availability of the highly-rated forward.
Dempsey is expected to leave Fulham after having been left out of Fulham’s first three games of the season.
Liverpool have been strongly linked with a move for the United States international in recent weeks.
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Chelsea legend Didier Drogba has revealed his top 11 Chelsea career moments during his recent interview on Chelsea TV.
The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.