The 22-year-old was linked with a surprise move to Stamford Bridge earlier this year after a ruptured cruciate ligament saw him make just three La Liga appearances last season.
However, Jese looks set to be handed a striker's role by new boss Rafa Benitez in the upcoming campaign after scoring a fine goal in the 3-0 win over Inter Milan on Monday.
I've never wanted to leave
Jese Rodriguez
And speaking to reports, the Spaniard insisted that he will not be on the move, explaining: "I've never wanted to leave.
"I'm very grateful to the coach for counting on me. He's shown he has faith in me. I'll try to make the most of every opportunity I get.
GETTY
Jese claims he wants to stay at Real Madrid this summer
"Coming back midway through last season as I had to do and not play, then play was far more complicated. I feel better. The injury is well behind me and I feel great.
"I don't mind where I play. I like all attacking positions so I can adapt easily."
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