The Spanish winger was one of the stars of this summer's Under-20 World Cup and impressed last season with 22 goals in Real's B team.
But Jese's contract runs out in June 2014 and that has sparked speculation he could be on the move this summer.
And the 20-year-old confesses he would not necessarily want to remain at Real due to his uncertainty over potential opportunities under new boss Carlo Ancelotti.
"I want to play, and I don't know if I'll get many minutes in the Real Madrid first team," Jese is quoted as saying in the Spanish media.
Earlier in July, Jese had revealed he planned to hold discussions with Real to establish what his future holds.
"I don't know what the club wants with me. I assume they will want to offer me a renewal but I don't know what I will do. I'm not going to lie about it," he told Marca before Spain U20s' exit at the hands of Uruguay in Bursa on Saturday night.
"I am calm about my future. I've had a good season and I'm doing well at the World Cup now. I'm relaxed.
"Once the World Cup is over, we'll open talks to discuss my future."