The Frenchman has been a key member of Chelsea's midfield over the past few years, helping them to the Premier League title in 2017 after winning it the previous season with Leicester.
However, according to La Parisien, Kante has fell out with manager Frank Lampard after the Chelsea boss refused to allow him to miss a day of training to attend a friend's wedding.
The pair clashed over the decision, with Kante subsequently questioning whether he wants to play under Lampard much longer.
In the same report by the French publication, Kante is claimed to be keen on a move to Real Madrid, a club he has supported since he was a child.
Chelsea and Inter had been in contact over the summer about a potential transfer, but no move materialised.
Zinedine Zidane is reportedly a fan of his compatriot and would be open to the idea of bringing him to the Santiago Bernabeu, though his main midfield target for the summer is 17-year-old Eduardo Camavinga of Rennes.
Up until the disagreement with Lampard, Kante had started every Premier League game of the season so far.