Tottenham Hotspur striker, Harry, has told the club to match his ambition to win trophies and keep improving, ESPN reports.
Kane has been linked with Real Madrid but insists he is happy with Spurs' progress at the moment.
"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, has admitted 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.
But Kane admits the club will find it hard to balance it all, as they seek to win their first trophy since 2008.
"It's something you assess along the way.
"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," he added.