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.
"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.
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.”
