The Hungary international, 21, has been outstanding for the Castilla this season and his exploits have linked him with Lille and Bordeaux.
Szalai's agent, Mihaly Laczko, told Foot Mercato: "There is nothing with these clubs. I was even surprised to see these rumors on the internet.
"Adam has a contract until 2010 and we'll look to see who will be the next manager of Real to learn more about the future of my player. But we are open to everything.