The Belgian attacker has previously been linked with several Premier League sides, and has now attracted the interest of the Spanish champions, too
The Belgium international has developed into somewhat of a Premier League star since joining the Cottagers in the summer of 2010, and his good performances have not gone unnoticed elsewhere.
"Real Madrid have contacted us and asked about Moussa Dembele's availability," De Visser stated to De Telegraaf.
"They are not the first big club to make enquiries about Moussa this summer, though."
Goal.com has previously revealed that Manchester United, Tottenham Hotspur and Arsenal have registered an interest in signing Dembele, while Manchester City and Chelsea are closely monitoring the attacker's situation.
The forward has a contract with Fulham until June 2013, but an offer in the region of €15 million could be needed to lure him away from Craven Cottage.