Arsenal and several other clubs are keen on signing the 29-year-old striker.
Dempsey’s current contract with Fulham is set to expire at the end of next season and he has been offered a new deal by the Cottagers.
Dempsey said: “We will see what happens. I am talking with the club but we will have to see what happens in the summer.
“I want to focus on this season and my football and other stuff can take care of itself after the season.”
Fulham boss Martin Jol said: “I can’t predict the future. We want to keep him and hopefully he wants to stay. We have offered him a very good deal.
“He knows he is very appreciated at our club. If we want to be a top side we need players who can score more than 20 goals a season.
“I have always had that – I can remember Luis Suarez scoring 53 for me at Ajax.
“He’s not at that level yet but for a wide midfield player who can play up front and score that many goals, it is unbelievable.”