Real Madrid have been heavily linked with a stunning move for Tottenham star Kane in recent weeks.
And Zinedine Zidane recently sparked rumours of a potential move after calling the England international the “complete player” prior to the Champions League encounter between the two sides.
Kane was flattered by the comments from the Real Madrid boss, stating he tries to use that as motivation to achieve his goal to become the world’s best player.
Real consider Kane as the perfect upgrade on Benzema, who will turn 30 in December, and has continuously been linked with a move away from the Bernabeu.
And El Gol Digital claim Real president Florentino Perez is ready to use Benzema in a potential deal to sign Kane.
The report claims Real would be expected to be close to £180million for the Tottenham forward if they were to offer straight cash, but the Spanish giants hope by offering to send Benzema to north London they can cut the price down to roughly £108m.
Kane swapped shirts with Cristiano Ronaldo after their Champions League match this week, and the 24-year-old admitted it will take pride of place in his house.
“I asked for his shirt at the end. He was a big role model of mine growing up. It’s a nice shirt to get. I will frame it.
“It was a great night for us. One we can be proud of — the fans can be proud of. The whole club can be proud.”
And Kane was typically self-deprecating when asked about giving his shirt to the Portuguese superstar.
He said: “I gave him my shirt. I don’t know what he’ll do with it!”