The Belgium international has long been linked with a move away from Craven Cottage, where he has shone since joining from AZ Alkmaar three years ago.
"I do not know (if I will leave)," he told Het Nieuwsblad. "Actually I can say nothing about.
"There was contact between Real and my agent. They wanted information, but that was it. Everything is still."
Press Association Sport understands clubs have expressed an interest in Dembele, but there have been no offers for the 25-year-old and, furthermore, Fulham would not entertain any.