The 25-year-old, who is thought to have attracted attention from a host of clubs this summer, has been known to be a target for the Spanish giants after the forward's representatives revealed their approach earlier this month.
"There has been contact between Real [Madrid] and my agent," Dembele told Het Nieuwsblad. "They have made an enquiry, but have left it at that so far.
"I don't really know [whether I will stay at Fulham]. I can't say much about it at this point. Everything is still possible."
The frontman has one year remaining on his current contract with the Cottagers.