The Belgium international has been strongly linked with a move away from Craven Cottage this summer, with the likes of Manchester United, Arsenal and Tottenham believed to be monitoring his situation.
Now Real Madrid have made contact with Dembele’s representatives, with a view to making a move for the 25-year-old as they are yet to agree a deal with Tottenham for long-term target Modric.
And Dembele, who is currently on international duty with Belgium, has admitted that he knows Real have made contact.
“My manager has already talked with Real,” he told Het Nieuwsblad.
“There have been contacts between my agent and Real Madrid. They have wanted information and that was it.
“I cannot say much else about it – everything is calm, but I cannot say where I will be playing.”
Dembele, who arrived in England as a striker, has moved more and more into a midfield role where it is believed Real see him playing.
And he admits that is where he sees himself, adding: “I feel more of a midfielder than striker. It is even my favourite position.”
Sky Sports understands that Dembele could be leaving Craven Cottage this month, and Real’s interest could alert his English suitors.
We also understand that the fact Dembele has a release clause of less than £20million is an appealing factor.