Kane, 25, is widely regarded as one of the best strikers in world football at the moment and has been subject to intense transfer speculation over the past 12 months.
Real Madrid and Manchester United are said to be long-term admirers of the prolific forward, who has won the Premier League Golden Boot twice and finished as top-scorer at the 2018 FIFA World Cup.
With Spurs currently 15 points off Premier League leaders Liverpool with eight rounds of fixtures remaining, the UEFA Champions League is seemingly their only hope of silverware this season.
And Kane admits, the desire for silverware might see him depart his boyhood club, whom he's netted 164 goals for in 249 games for since making his full first-team debut in 2014.
"I've always said as long as the club is moving in the right direction and showing the right ambition, I want to be part of the journey," he told ESPN FC.
"A lot of people look at it and say this is maybe the best team we've had, maybe the best team we'll ever have and the best manager, but it's important that we have something to show for it."
With Spurs having built a new stadium and not adding new players to the squad over the past two transfer windows, the Three Lions skipper concedes there's a level of understanding on the lack of squad investment.
"It's not just when we look back in 10 years, we had a great team. It's, 'Look what they did. Look what they won.'
"The challenge for us is, can we keep going up and up and up? It's going to be difficult in the next couple of years with the stadium and the finances."
Kane has scored 22 goals in 37 games for England since earning his first senior cap against Lithuania four years ago.