The club will re-enter the Europa League this season but the 28-year-old striker - voted Fulham's player of the season for 2010/11 - said he would jump ship for a chance to play in the Champions League.
"Right now, I'm thinking about Europe and playing in Champions League - at least experiencing that in my career, being in Champions League," said Dempsey, who holds the Fulham record for goals scored.
"That's a goal. That's every player's goal. Every player wants to win trophies and play at the highest level possible. If someday I get the opportunity to play for a big club in the Champions League, that would be great. I'd be lying if I said that wasn't a dream."