The teenager has seen his stock rise after Spain's Under-19 triumph, with Los Blancos acting fast to deter any potential suitors for the promising striker
The 19-year-old scored the winner in Spain's Uefa Under-19 European Championship final against Greece last Sunday, also taking the top scorer award.
With increased interest from Arsenal, Manchester City and Benfica, Jese's agent, Gines Carvajal has sought to cool interest in the Madrid protege.
"Jese last year signed a contract until 2014 and a buyout clause of €40 million. In addition, Madrid does not intend to sell him. He is untouchable." Carvajal was quoted as saying by AS.
The report in AS states that Jese will continue featuring for Real Madrid Castilla for the time being, eventually being developed for a first-team place later in the season.
Jese returns to training on July 25 in the Spanish capital, but it remains to be seen whether he will participate in the club's US tour.