The 12-time European champions are said to be keen on signing Spurs' top marksman this season, but are aware that they will face major resistance from the Premier League outfit.
Kane has scored more goals for club and country than any other player in Europe in 2017 and is the favourite to pick up the Golden Boot again this season. Real are ready to make a move for the England international in the summer, but Tottenham remain adamant that he is not for sale.
According to Spanish publication Sport, Florentino Perez is ready to add Gareth Bale as part of the deal to secure Kane's signature. The Spanish capital club's president is hoping that the English club's interest in re-signing the Welshman could tempt them into coming to the negotiation table.
The report claims that Real are willing to pay €150m (£133m)-plus-Bale to sign Kane after realising that Tottenham will not allow the striker to leave for less than €200m. It is being suggested that the club have already initiated contacts, but at the moment Daniel Levy has responded with an emphatic no in terms of a potential sale.
However, Real believe that their initial efforts will put them in pole position if the striker becomes available as they are aware that they will face competition from Manchester United, who have also been linked with a move in the recent past.
Mauricio Pochettino, meanwhile, has made it clear that the club have no intention of selling Kane, but admitted that they will only consider it if the player pushes for a move similar to Gareth Bale and Luca Modric, who asked for a move when Real made their interest known.
"If you look at it from the personal side, if the player asked to go like Modric or Bale, we would have to see but today that has not happened," Pochettino said, as quoted by the Mirror.
"I hope that Harry Kane will be here for many years and bring lots of goals and victories and win some titles, that's what we want,
"Being responsible for a club like Tottenham, I would say if Real Madrid came, we would tell them we do not want to sell him. He would stay here and he would have to understand," the Argentine coach explained. "Kane doesn't have a price because we love him here. He is off the market."
Tottenham are making every effort to ward off interest for their top scorer and according to the Daily Mail, their latest effort is to offer him a new improved deal that will see him become the best paid English player in the Premier League.
Kane signed a new Spurs deal in December 2016 which made him the highest paid Spurs player at £110,000-a-week, but that is a far cry from the top earners in the English top-flight. The report claims that the White Hart Lane outfit are ready to smash their wage structure and offer him a new deal worth £200,000-a-week taking him over Raheem Sterling, who is currently the best paid Englishman.