Van Damme has been a key player for Anderlecht this summer, but will be out of contract next summer.
Fulham manager Roy Hodgson can land him in a £2million deal, according to the Daily Mirror.
The 26-year-old said: “I have received a concrete offer from a club in England, although I won’t yet say which one.
“I have always said that I will not pass up a second chance to play in the Premier League.”
Anderlecht general manager Herman van Holsbeeck added: “Jelle has to decide whether he wants to make a financial coup or take a further upward step with us.
“He is a modern midfielder, and very important with his enthusiasm, strength and stamina – and I can still see him staying if he is ready to make a compromise on his salary.”
