According to Cadena Ser, Los Blancos are looking to prise Kane away from Tottenham and reduce their reliance on Karim Benzema.
The Frenchman, who turns 34 this year, has spent 12 years at the Bernabeu, winning La Liga three times and the Champions League four.
He was originally intending to stay with Dortmund for another year, but is contemplating leaving the club this summer if they fail to qualify for the Champions League.
In the event that he decides to move on, there will be no shortage of suitors for the Norwegian striker, who has scored 49 goals in 49 games since moving to the Bundesliga.
Mbappe is the other player earmarked as the star of the next generation, ready to overtake the ageing Cristiano Ronaldo and Lionel Messi.
In contrast, Kane is entering the prime of his career and has enjoyed a brilliant season in difficult circumstances for Tottenham, scoring 27 goals and registering 16 assists.
His relationship with Son Heung-Min has continued to blossom, with both of them assuming a large share of Spurs’ attacking burden.
The England captain remains as clinical as ever in front of goal and has Alan Shearer’s Premier League record in his sights, having moved within 100 of his total after converting another penalty against Aston Villa on Sunday.
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