Having only started three La Liga matches last term - partially due to injury - Jese has been linked with a summer exit this close-season, but the Madrid youth product insists he never entertained the idea of moving on.
"I've never wanted to leave," he told reporters.
"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."
Jese then went on to make it clear that his knee injury from last season is well behind him after scoring his first goal of 2015-16.
The 22-year-old scored the opener for Rafa Benitez's men in their 3-0 win over Inter in China on Monday, showing a classic poacher's instinct as he brought down Marcelo's cross in the box in the 29th minute before cutting inside a defender to score.
Having missed the first half of the 2014-15 season with a ruptured cruciate ligament, Jese declared he is ready to start the new campaign in top gear.
"Coming back midway through last season as I had to do and not play, then play was far more complicated," he said.
"I feel better. The injury is well behind me and I feel great."
While Jese has generally played on the left under previous coaches, he is enjoying the new challenge of leading the line.
"I don't mind where I play. I like all attacking positions so I can adapt easily."