Everton are among several clubs interested in the Frenchman, who has one year left on his contract.
Dembele joined Fulham from Paris Saint Germain in 2012 and impressed during his 15 appearances for the club last season.
The France Under-19 international said: “I’m very flattered by the interest from top level clubs. I always want to improve, but I love Fulham and I respect Fulham, so I work hard to do my best.
“I’m very good at Fulham. I know everyone and I’m going to take my time to make the right choice.”
Dembele also made reference to the role of his team when making the decision whether to leave the Championship club.
He added: “I want to take my time with my agent, my family and the people around me to make the right choice.”