The Fulham midfielder reiterated his desire to play in Europe's premier competition at some point in his career but insists he will give his best for any team he plays for
The American signed for Fulham in 2007 from New England Revolution and has enjoyed his most prolific season to date, scoring 23 goals in all competitions.
His blistering form has reportedly attracted interest from the likes of Arsenal, Manchester United and Tottenham ahead of the summer transfer window.
Dempsey has one year remaining on his current contract and, while speculation surrounding his future continues to circulate, the 29-year-old insists that he will give his all for his club.
"What I do is focus on the teams that I play for and I give my heart to them, work as hard as I can to try to make the most of my time and make the most of the career that I have left," he told reporters.
"The transfer window is open until August 31. It's no secret that I would like to play Champions League one day in my career.
"If it's meant to be, it will be."
Dempsey is currently training with the USA squad ahead of Thursday's friendly with Brazil, and current manager Jurgen Klinsmann has encouraged the forward to look for a bigger club.
"His goal is the right goal," the German coach said last week. "If he has the opportunity to go a Champions League team, that's the creme de la creme in the world of club soccer, then you've got to do that."