The Bianconeri are looking for a replacement for injured midfielder Claudio Marchisio this summer, and have switched their attention to the French enforcer after seeing a bid for Javier Mascherano blocked by Barcelona.
Kante enjoyed a hugely successful first season in English football, playing an important part in the Foxes' surprise Premier League title win.
Leicester are unsurprisingly keen to keep hold of the 25-year-old, but his impressive form has seen him linked with several top clubs.
Goal.com journalist Romeo Agresti claims Kante's representatives have offered him to Juventus following talks over the last few weeks, but the size of the Parisian's buyout clause at the club has not yet been disclosed to the Italian side.
The Metro had previously reported that the value of his clause was in the region of £20 million, but Juve director general Beppe Marotta wants to establish a concrete figure before deciding whether to submit a bid.