England's elite have all been tracking the Belgium international, as Goal.com exclusively revealed first the interest of Arsenal, Liverpool and Tottenham before Manchester United, Manchester City and Chelsea all joined the race in May.
|40/1||Fulham are 40/1 with William Hill to finish in the Premier League top four
"Personally, I would like to go to the top. I think every player wants that. But I have the confidence to say that I want to play at a top club one day," the 25-year-old told Sport 1.
However, Dembele moved to calm Fulham fans' fears over his immediate future, adding: "[Fulham] is a good team. We have had two good matches now so it also makes sense to play here.
"As long as there is no bid, nothing happens."
The Belgian confirmed earlier in August that he is also the subject of interest from Spain after Liga holders Real Madrid made contact with his agent.