Kane, who is ranked the world's No. 1 striker by ESPN FC, has been linked with Real Madrid but remains happy with Spurs' progress at the moment.
Schoenfeld: Kane wants to conquer Premier League ... and NFL
"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 said.
Tottenham chairman Daniel Levy said the move to a new stadium will not affect the club's spending plans, despite Spurs not signing a new player for two transfer windows -- and Kane admits the club have a difficult balancing act looming in the next few years as they seek to win their first trophy since 2008.
"It's something you assess along the way," he said.
"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.
"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."
Spurs coach Mauricio Pochettino has also been linked to Real Madrid, as well as to Manchester United, and Kane highlighted the Argentine's ambition as a factor in their combined success.
"We [him and Pochettino] both want the same things," Kane said. "We both want to push and push and push, and work and work.
"We'll just have to see what happens this season, and go from there."
On Thursday, Kane received the MBE award on Thursday for services to football after leading the national team to the World Cup semfinal in Russia last summer.
Prince William, the president of the English Football Association, presented the 25-year-old Tottenham striker with his medal at Buckingham Palace after Kane was included in Queen Elizabeth's 2019 New Year's honours list.