Kane, who won the Golden Boot at the World Cup and has scored 135 goals in 187 Tottenham appearances, signed a new contract in June taking him until 2024.
As one of the world’s best strikers, interest in Kane is high but Spurs chairman Daniel Levy has strongly resisted all approaches.
Following Cristiano Ronaldo’s transfer to Juventus, Real Madrid are in the market for a marquee player.
But Spanish newspaper AS claims the Champions League winners view the possibility of signing Kane as “almost impossible”.
The report says Real recognise they would need to make a “very high” offer to even tempt Spurs into selling Kane.
But is also claimed Real have doubts over Kane’s ability to adapt to La Liga.
Paris Saint-Germain striker Edinson Cavani is considered to be the most feasible signing and it is said he would be “very receptive” to joining if he received an offer.
Spurs will move into their new stadium this season and former striker Dimitar Berbatov doesn’t see Kane leaving soon.
Berbatov told Betfair: “I don’t see Kane leaving for Real Madrid, not at this current moment.
“The club will have a new stadium soon which shows ambition to him and the squad is building on top of their foundation.
“He’ll stay and fight for silverware for now, but further in the future, I cannot be sure.”
TOTTENHAM TRANSFER NEWS
Manager: Mauricio Pochettino
Position last season: 3rd
Ground: Wembley/Tottenham Hotspur Stadium
Players In: –
Players Out: Keanan Bennetts (Borussia Monchengladbach, undisclosed), Anton Walkes (Portsmouth, undisclosed)
Key Man: Harry Kane
Chances: A top-three finish was heralded as a success last season after Spurs played at Wembley, and Mauricio Pochettino’s side will be expected to repeat that when they eventually settle into life in their new home. Nine of the Spurs’ squad were involved in the World Cup semi-finals or later, so much will depend on how they all return after a hectic, emotional summer.