The Blues have clinched the 2016-17 Premier League title with relative ease and will face Arsenal in the FA Cup final later this month.
It has also proven a fruitful period for Kante, who now has back-to-back top-flight championship medals with different clubs after his heroics for Leicester City last season.
The France international, who won the Professional Footballers' Association Player of the Year in April, now has his sights on the Champions League and the League Cup too.
"Next season will be a new challenge because we are going to try to keep the title, to win the two cups (FA Cup and League Cup) and also we'll have the Champions League," Kante told reporters at the Landmark Hotel on Thursday night.
"For a club like Chelsea, we want to win everything, we're going to try and win everything. It's a new challenge for everyone."