There's every chance he'll still be at Fulham next season, but what if he was to make the journey north and play for Liverpool?
I'm going to look at five things to consider if Dempsey moves to Anfield.
Feel free to leave any comments below.
Although it's rare in this day and age, player-plus-cash deals can still work.
I don't know what Fulham's valuation of Clint Dempsey is, but I'd say it'd be £10 million plus. That's pretty fair when you consider the amount of goals he scored for the Cottagers last year.
If Liverpool were to offer that, Fulham might want someone else in return. Why not offer Joe Cole? Sometimes it just doesn't work out for players at clubs and that might be the case with Joe. He isn't a bad player, but maybe it's just never going to happen.
At this stage in his career, Joe needs to be playing first team football every week and with all due respect, I think there's more chance of that happening at Fulham than Liverpool.
As it stands, Liverpool already have a hell of a lot of midfielders.
Steven Gerrard, Charlie Adam, Alberto Aquilani, Joe Cole, Lucas, Jonjo Shelvey, Jay Spearing, Stewart Downing and Jordan Henderson are already on the books.
Luis Suarez and Craig Bellamy can also fill in behind the striker in an advanced midfield role, so it stands to reason that some of those players would have to make way.
With all due respect, could Clint Dempsey cut it at Liverpool?
There have been highly-rated players at other clubs who couldn't do it at a "bigger" club.
For example, Diego Forlan was highly rated when he signed for Manchester Utd all those years ago, but it just never worked out for him.
When he moved to Spain and then Italy, Forlan proved what a class act he was.
Dempsey is a tremendous Premier League player, but would he be as successful at Liverpool as he's been at Fulham?
One of the best things about Clint Dempsey is his versatility.
He can play across the midfield, behind the striker or even up front if he needs to.
Sometimes, Liverpool have had to play midfielders out of position in order to accommodate them, but they wouldn't have that problem with Dempsey.
He's happy playing with either his left or right foot and that could be a key factor in determining his potential arrival at Anfield.
His goal return for Fulham last year was outstanding and if there's one thing Liverpool were short of last season, it was goals.
Adding Dempsey to the squad might just make the difference between finishing in Europa League and Champions League places.