Kante was voted the best player in English football by both the Professional Footballers' Association and Football Writers' Association last season for his influential role in Chelsea's title victory.
Chelsea coach Antonio Conte believes he has already begun the campaign justifying that accolade.
But Kante, it seems, sees things a little differently.
"I don’t feel like the Player of the Year. I don’t really care about it when I play on the pitch,” he said.
"I think in football, when one game passes we need to forget to keep improving.
"I think last season was amazing for me and the club, but this was the past and we need to focus for the future.
"I just try to always do my best when I’m on the pitch, try to improve in training and give my best in the game."
Meanwhile, Kante is convinced France team-mate Tiemoue Bakayoko can comfortably fill the void left by Nemanja Matic's departure to Manchester United.
Matic made it clear he wanted to leave for Old Trafford in the summer and he was sold for £40m.
But Chelsea soon replaced him with Bakayoko's arrival from Monaco for the same fee and the 23-year-old, who is six years younger than Matic, has impressed in three appearances so far.
Kante added: "For sure, Nemanja Matic was a good player for us. I know he was in Chelsea for many years.
"I had the chance to play one year with him and he was a very good player for me. We spent a good season together.
"He [has] left now, he plays for United but Bakayoko has come and I think he’s a good player, and that we can do very well with him."