According to Fichajes, Los Blancos have identified the 31-year-old midfielder as a potential target.
Kante will be a free agent at the end of the campaign, and the Frenchman could be available for a reasonable price this month. The La Liga champions might hope to take advantage of his situation and ready to bring the veteran defensive midfielder to the Bernabeu this year.
The European champions might need to come forward with a lucrative offer to tempt Chelsea, who have been linked with a number of players this month.
The Blues have managed to strengthen their defence and attack this month but the midfield remains an area of concern.
It will be interesting to see if Chelsea boss Graham Potter can sign a quality central midfielder before the January transfer window shuts down.
Kante has made 262 appearances for Chelsea.