The Belgium international is continually being linked with a move away from Fulham, and has now seemingly caught the attention of the Liga champions
The Fulham striker's representative recently revealed that the Blancos had made an enquiry, and the versatile attacker has now admitted that there has indeed been contact.
"There has been contact between Real [Madrid] and my agent. They have made an enquiry, but have left it at that so far," Dembele was quoted as saying by Het Nieuwsblad.
"I don't really know [whether I will stay with Fulham]. I can't say much about it at this point. Everything is still possible."
Dembele, 25, has a contract with the Premier League side until the summer of 2013, and is continually being linked with a move to a bigger club.
Goal.com revealed earlier this summer that Manchester United, Arsenal, and Tottenham Hotspur are all interested in signing the former AZ star.