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.
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.