The 23-year-old's agent, Mino Raiola, had previously claimed his client was "99.9 per cent" certain to extend his stay at Goodison Park, with reports of a five-year deal worth around £140,000 a week on the table.
However, having recently admitted a frustration over a lack of trophies won during his career, the Belgium international has now given the strongest indication yet that an extension has been rejected.
"The decision has already been made so I can't talk about that," Lukaku told reporters.
"There is nothing wrong with ambition. You have to embrace it and where you are as a footballer.
"Sometimes people will mistake things that I say but it's just ambition that I have; I want to win titles and trophies and I don't think people should take that as arrogance - people should embrace it.
"This is what footballers need to achieve if they want to become the best, and I think young kids need to learn that too."
Standard Sport understands Chelsea manager Antonio Conte has Lukaku on a shortlist of summer striker targets, which also includes Real Madrid's Alvaro Morata.
However, the former Blues player is expected to cost a British record fee, eclipsing the £65 million Barcelona paid for Luis Suarez a little under three years ago.
He continued: "I have made a long way until now but the road is still long and I know I have to improve and get better.
"I want to help Everton as much as I can, as well as the national team. I think a lot of stuff can be achieved."