The American winger has sparked an interest in various top four Premier League clubs.
According to The Sun, Tottenham and Arsenal are just two of the clubs looking to sign "the £10million-rated ace"
Dempsey has scored a total of 21 goals this season, 15 in the Premier League, surpassing Louis Saha's record of 13 goals set eight years ago.
The American hasn't publicly said anything about his future; he only said "We'll see what happens. Some of my best memories have been at Fulham".
Fulham will most likely want him to commit to the club, as he only has one more season left in his contract with the London club, Fulham manager Martin Jol has apparently offered the American star a 'bumper new deal to stay' "I still have this season and one more at the club. I'm talking with Fulham but we'll see in the summer".
However the 29 year old has other things on his mind "I just want to focus on my football and helping the club finish in the top half. That other stuff can take care of itself." He said.