The Telegraph says having helped Leicester to a fairytale title triumph in 2016, Kante was a hot property in the transfer market.
The £30million deal was completed after then-Blues boss Conte phoned the midfielder to convince him that he would win a second Prem crown in a row at Stamford Bridge.
It has previously been claimed that a row over agents' fees led to the Gunners backing out and signing Granit Xhaka instead.
While the Swiss midfielder has been unable to threaten the Premier League trophy, Kante went on to lift it that year with Conte's Chelsea.
The 30-year-old has tasted success in Europe too when winning the 2019 Europa League.
Conte has just led Inter Milan to a first Scudetto triumph in over ten years.