The American midfielder, 27, excelled as Fulham reached the final of the Europa League last season, before playing a key role as the USA progressed to the last 16 of the World Cup in South Africa.
And Lyle Yorks, who represents Dempsey, believes his client could be tempted to try his luck at a bigger club following the departure of inspirational manager Hodgson to Anfield.
"There is a lot of interest from big clubs in Europe in Clint. And now you’ve got Roy Hodgson leaving for Liverpool... so there’s a lot of different things going on," Yorks told the MLS website.
Recent press speculation has suggested Dempsey could be earmarked by the new Liverpool boss as a potential replacement for Yossi Benayoun, who last week left Anfield for Chelsea.
The Reds would face stiff competition for the Cottagers' midfielder, who caught the eye of several major clubs on the continent during Fulham’s successful Europa League campaign, which included a spectacular goal against Juventus.
Indeed, reports in Italy during the World Cup had linked Dempsey with a move to Serie A side Napoli. However, Yorks dismissed the speculation, simply stating: "We don’t have an offer from Napoli."
“We’ve got, in Italy, a major club and in France a major club. And in the Bundesliga a club. We’ll be sorting through them in the coming weeks and also seeing what happens at Fulham.
“There’s direct contact and discussions, but first they’d have to agree with Fulham.”
Roy Hodgson faces the unenviable task of steadying the ship at Liverpool, with star names Steven Gerrard, Fernando Torres and Javier Mascherano all being linked with summer moves away from Anfield.
By James Martini
