Kane only signed a new deal at Spurs in December 2016 to commit his long-term future to Pochettino's side until 2022.
The Guardian and other publications reported at the time that that the England international was ready to earn up to £120,000-a-week after Tottenham agreed to double his previous salary.
However, his long-term future at the Premier League side has been trough into question amid reports in Spain claiming that Real Madrid president Florentino Perez had identified the striker as his next Galactico signing.
The England international has enjoyed an impressive start to the new campaign, scoring 13 goals in 12 appearances for Spurs, including five in three Champions League games.
It has been said that Perez even made an informal enquiry to Tottenham Chairman Daniel Levy over Kane when Real Madrid faced the Premier League side in the Champions League last week.
The chiefs of both clubs enjoy a very good relationship, having already conducted business in the recent past when Los Blancos signed Luka Modric and Gareth Bale.
But Perez has ruled out making a new move to sign another Tottenham player after jokingly claiming that Levy would demand a world record €250m (£223.2m, $294m) fee to cash in on with the 24-year-old striker.
"No, honestly [signing Kane has not passed through my head] He is a great player and is young. He has many years ahead to progress but we are delighted with [Karim] Benzema and with all of the team," Perez said to Cadena Cope.
"No, [I didn't ask Levy for the price] because if ask him a price he would have told me that he is worth €250 million. I know him well. We became friends during the time it took us to sign Luka Modric and Gareth Bale. We signed them on deadline day and ended up making a good friendship. Whenever we win a Champions League he tells me the same thing: 'Congratulations for the Cup that you've won with my players'.
Speculation linking Real Madrid with Kane have increased in recent days with Benzema having endured a difficult start to the season in front of goal.
Last week Gary Lineker even tweeted that the France international was "a tad overrated" following his disappointing performance during the draw with Tottenham in the Champions League.
But Perez lavished praise on Benzema after the striker at the weekend came off the bench to help Real Madrid to secure a 3-0 victory over Malaga by setting up Marcelo's third goal with a sensational assist.
"[Lineker comments] does not bother me. Everyone has the right to say what they want but I think people only judge [Benzema] by his goals. Against Malaga he gave a spectacular masterclass. I always say that Benzema is a mix of Zidane and [the Brazilian] Ronaldo. He scores goals like Ronaldo and have the touch of Zidane. It is a luxury [to have him with us]," Perez added.