The striker also warned Mauricio Pochettino's team - who trail leaders Manchester City by 21 points - need to start winning trophies if they aim to keep him.
Real Madrid are big admirers of the super striker and Kane knows he would be able to triple his £100,000-a-week wages with a move to the Bernabeu.
In December 2016 Kane signed a new contract with the north Londoners that ties him to the club until 2022.
After scoring twice in Sunday's 3-0 FA Cup defeat of AFC Wimbledon, Kane knocked back reports of Spurs being in talks with him about a new, improved deal. "None are planned, that I know of," he said.
And Kane, who had been with Spurs since he joined their academy in 2009, said: "I think if a player wants to go then why would you stop him?
"He's not going to be in the club, he's not going to play every game, he's not going to put his heart on the line."
Kane, 25, has yet to win any trophy with Spurs and he warned the club needed to step up if they wanted him to stay.
"I've always said keep progressing, keep getting better, start winning trophies," he said.
"That's the aim, as long as the club keep doing that then, yeah I'm happy here."
This month centre-back Virgil van Dijk got the move he wanted when Liverpool signed him for £75m from Southampton, who thwarted the Anfield approach in the summer and even reported them for an alleged illegal approach.
And Liverpool have just sold their star player, Phillipe Coutinho, to Barcelona for £142m, despite boss Jurgen Klopp claiming in August the playmaker would not be sold "for any price".
Kane, who has bagged 26 goals this season, said: "From the Coutinho point of view I think he's been very professional in the six months he has played this year and, look, Liverpool have got a good offer from Barca and accepted it.
"So I wouldn't say they're powerless, but I can see why if a player wants to go you would let him go."
Pressed on whether players should honour their contracts, Kane added: "Again, it's a matter of opinion. It's hard to talk about but the situation at the time.
"You kind of assess it and I suppose see what's best for the team and what the manager wants to do and you go from there really."