It has been reported that former Chelsea boss Antonio Conte was interested in taking Kante to Italy this summer, with the midfielder having endured an injury-hit campaign at Stamford Bridge last season.
The Mirror claimed that the two clubs had held initial talks over the Frenchman, but Chelsea were demanding a fee of £80 million.
Kante has been an influential player since his arrival in England in 2015.
The 29-year-old won back-to-back Premier League titles with Leicester City and Chelsea, before lifting the World Cup with France in 2018.
But questions arose over the role he played for the Blues under former head coach Maurizio Sarri.
Injury restricted the midfielder to 22 Premier League appearances last season, leading to speculation that his future could lie away from Stamford Bridge.
However, Ausilio has ruled out the possibility of the Frenchman arriving at the San Siro this summer.
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“We’ve never started anything to sign Kante from Chelsea. No chance. He’s not a target,” he told Sky Sports Italia.
Kante has played a total of 170 times for Chelsea since his move to Stamford Bridge in 2016, scoring 11 goals and providing a further seven assists.
The Frenchman was named as PFA player of the year during Chelsea’s title win in 2017.