The 24-year-old has attracted interest from major European clubs in recent seasons, with Real Madrid's former president Ramon Calderon stating in October that he expected the Spanish club to try to sign the forward.
Asked what Tottenham needed to do to ensure he commits his long-term future to the club, Kane said: "We want to start winning trophies so that's the aim. As long as the club keeps doing that then I'm happy here.
"I've always said, just keep progressing, keep getting better."
Tottenham lost to Chelsea in the 2015 League Cup final in Kane's breakthrough year and have not won a major trophy since lifting the League Cup in the 2007-08 season.
The Londoners sit 21 points behind Premier League leaders Manchester City with 41 points from 22 games and Kane believes the FA Cup offers them a realistic chance of a trophy.
"We want to win a trophy somehow and this is a competition we're looking at to do that," he said.
Tottenham return to league action on Saturday with the visit of ninth-placed Everton.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
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