The striker's goalscoring exploits for club and country since his breakthrough at Spurs have earned attention from the Champions League holders, but chairman Daniel Levy is said to be demanding £200 million for him.
Mauricio Pochettino's side have already beaten Madrid this season and sit three points ahead of them in their Champions League group amid a bright start to their season.
Having been at the club since the age of 11, the two-time Premier League Golden Boot winner says he is in no rush to leave a promising Spurs team and feels he could hang up his boots as a one-club man.
"My goal is to play my entire career only for Tottenham," he told Bild am Sonntag.
"We have a fantastic team, a great coach, a professional training centre and we're getting a new stadium. At the moment, everything suits me here and I'm happy."
Tottenham continue their European campaign on Tuesday when they take on Borussia Dortmund, who have just two points from four games in the competition.
Pochettino's men beat their German counterparts 3-1 when they met at Wembley in the first game and Kane is confident of getting the better of them despite identifying two key players.
"Marco Reus and Pierre-Emerick Aubameyang have both caused the a stir for many in Europe in the past few years," he added.
"Dortmund have a lot of pressure now and have to win both matches to get a chance to progress.
"We are not afraid, we have found our style, we are now also winning away from home and we are cleverer."