The Blues ace has been linked with a move to the LaLiga giants over the past year.
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Real Madrid boss Zinedine Zidane is believed to be a big fan of Kante, who won the World Cup with France last summer.
Spanish outlet Defensa Central claim Chelsea have agreed to let Real know when a club bids for Kante, or if they decide to sell the 28-year-old.
The verbal agreement allegedly comes after Real did not pursue the former Leicester star in the summer transfer window following the signing of Eden Hazard.
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Chelsea were adamant that they would not lose two of their star players in the same window.
Kante has missed Chelsea’s last two games with an ankle injury, while he also did not feature in France’s Euro 2020 qualifying wins over Albania and Andorra as he fights to recover to full fitness.
Prior to the international break, Blues boss Frank Lampard was hopeful Kante could return to his side against Wolves this weekend.