Spanish publication 'Diario Gol' reports that the Spanish champions are considering offering Spurs Gareth Bale, Karim Benzema and Luka Modric in exchange for Kane.
Real had previously expressed an interest in the 24-year-old but were put off when Spurs chairman Daniel Levy informed them that the player would be going nowhere unless a club stumped up €200m.
Kane has started the season in superb form, scoring 11 goals in just nine appearances and was yestersday announced as one of the nominees for this year's Ballon d'Or.
That sort of form is what has attracted 'Los Blancos', but with Real unwilling to shell out €200m they have attempted to put together a swap deal.
The aformentioned source claims that Bale and Benzema would be the first players included and that if Spurs still found the deal to be of insufficient value then Florentino Perez would then also add Modric into the bargain.
Perez believes that the move makes perfect sense as Bale's injuries have devalued him somewhat, meaning that a sale is unlikely, Kane would act as Benzema's replacement and Dani Ceballos or Mateo Kovaci could step into the void created by Modric's departure.
However, with Real Madrid boss Zinedine Zidane unwavering in his support for the 'BBC' and with the Frenchman having described Benzema as 'untouchable' in the past, it is hard to believe that this story carries any weight.