The 31-year-old is one of the most prolific strikers of the past decade but is yet to win a piece of major silverware.
Kane looks set to break his duck at the end of the season, with Bayern Munich sitting six points clear at the top of the Bundesliga title.
Speaking to ESPN, the England captain said: "I've done a lot of things I've wanted to do in my career so far.
“Of course, I know the team trophy is the one that everyone will refer back to, but ultimately, you know, you have to do your best in every situation.
“And I feel like I've done that. From when I set out, it was always about how consistent I could be.
"I looked at the greats of the game and what made them great, and it wasn't just doing it in spells, it was doing it year after year. And that was a big drive of mine to be able to consistently be one of the best players in the world.
“And that drive will be with me until the end of my career, whether I finish with one trophy or 20 trophies. Ultimately, it won't change my mindset and what I want to achieve and how I try and achieve it."