According to the player, the Portuguese manager called Kante in a bid to convince him to move to Old Trafford for an alleged £25m-plus.
But despite the personal plea, Kante turned down the offer.
Kante said: “It was amazing to have Mourinho call me, even though I’d been warned before how he would appeal to me.
“I listened to his arguments about why I should move to United.
“But at that time I was hesitant between staying at Leicester or leaving for Chelsea.
“My discussions with them were already well underway. But when I spoke, I had a good feeling with Conte.”
But it was eventually the Italian who secured the player’s signature, bringing him to Stamford Bridge for £29m.
Kante was Chelsea’s first signing of the summer and has starred in every game for the Blues so far, recreating the sort of form that helped guide Leicester City to the Premier League title last season.
Kante added: “At Chelsea I’m in a star-studded dressing room.
“Being the star of the game doesn’t interest me. That’s the highest level, unless you have exceptional qualities.
“Yes, I feel I’m a pretty complete player, but I’m not an outstanding player.
“Someone like Riyad Mahrez, yes, he has a real technical talent.”
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