The 19-year-old has been linked with the likes of Arsenal, Manchester City and Benfica after impressing for Spain at the Uefa Under-19 European Championships.
Rodriguez’s agent, Gines Carvajal, has tried to cool interest in his client.
Carvajal told AS: “Jese last year signed a contract until 2014 and a buyout clause of 40 million euros.
“In addition, Madrid does not intend to sell him. He is untouchable.”