England captain Kane has often spoken of his desire to win titles with Tottenham but reports have suggested he may look elsewhere if his ambitions are not met.
Speaking on a live Instagram broadcast with Sky Sports pundit and ex-Spurs midfielder Jamie Redknapp, Kane said: "Obviously I get asked this question a lot.
"It's one of those things – I couldn't say yes and I couldn't say no.
"I love Spurs, I'll always love Spurs but I've always said if I don't feel we're progressing as a team or going in the right direction, I'm not someone to stay there for the sake of it.
"I'm an ambitious player, I want to improve, get better and become one of the top, top players. It all depends on what happens as a team and how we progress as a team.
"So it's not a definite I'm going to stay there forever but it's not a no either."
Meanwhile, Spurs confirmed Son Heung-min and Steven Bergiwijn are to be allowed to return to South Korea and Netherlands respectively.
Son has travelled home for personal reasons, while Bergwijn is awaiting the birth of his child.
Spurs said "both players will continue their individual rehabilitation and training programmes during their time away" with the Premier League still suspended due to the coronavirus pandemic.