The 25-year-old has been linked with the likes of Arsenal, Tottenham and Manchester United in recent weeks.
The Belgian has impressed for Fulham since joining the club from Dutch side AZ Alkmaar in a £5million deal in 2010.
“Real Madrid have contacted us and asked about the possibility of signing Moussa Dembele,” Dembele’s agent Jan de Visser, of management agency Sport International, said in De Telegraaf.
“They are not the first big club who have contacted us this summer for him.”
