According to Onda Cero (h/t Sky Sports), the two clubs held informal discussions about a potential deal when they met in the UEFA Champions League last week. Spurs were said to have quoted a £200 million asking price to the European champions.
However, when asked about Kane on Cadena Cope show El Partidazo (h/t Sky Sports), Perez denied that was the case and suggested Spurs would want even more for their star striker:
"Signing [Kane] has not passed through my head. He is a great player, and in addition he is young.
"He has many years to progress, but we are delighted with [Karim] Benzema and with all of the team.
"I didn't ask Tottenham's president for the price because he would have told me that he is worth €250 million."
According to Jose Felix Diaz of Marca, Madrid have been keeping an eye on the development of the Spurs star. But it's claimed the Los Blancos hierarchy "were not dazzled" by his performance in the game at the Santiago Bernabeu Stadium.
If Madrid have been keeping tabs on Kane over the past few years, they will have been impressed at some point, as the 24-year-old continues to light up the Premier League.
As noted by the Champions League Twitter account, in 2017 he's been in stunning form in front of goal:
Typically, he's the type of player Madrid would target. Kane leads the line with power and poise, is adept at bringing others into the game and can score many different types of goals. He would be a perfect replacement for someone like Benzema.
At the moment, Madrid would potentially benefit from having another centre-forward in the squad. Cristiano Ronaldo is at his best when he has a partner in the final third, whereas Benzema is adept at operating as a lone striker.
As former England and Barcelona forward Gary Lineker noted, it appears Madrid have full faith in the Frenchman:
But Madrid always want the best players in the world, especially those who are on an upward trajectory in their careers. Kane ticks both of those boxes.
The rate at which the England international has found the back of the net in 2017 has been sensational, and if he continues to net at such an incredible rate, links with the biggest clubs in the game will crop up frequently. Spurs will be aware that at some point they will face a big fight to keep Kane around.
It would be a surprise to see Madrid make their move next summer based on Perez's comments. And even for a fee of €250 million (£223 million), you sense Spurs would be reluctant to sell their homegrown talisman.