Inter have already failed with a bid which involved cash and Marcelo Brozovic, in an effort to sign the Chelsea star this month, but have not given up hope of landing him.
Frank Lampard has claimed that he wants to keep Kante and expects Chelsea to reject any more bids from Inter for the Frenchman.
But Inter are confident that a deal can be done and most importantly they are aware that the player is keen on the move.
According to Italian daily Gazzetta dello Sport, Kante is keen on the move to Inter and wants to play under his former Chelsea manager, Conte.
The 29-year-old has given his approval to the proposed switch and is now waiting for Inter to come up with an appropriate offer.
Despite Lampard’s public assertions, it has been claimed that Chelsea will sell Kante if they receive a bid of €50m.
Conte has identified the Blues midfielder as his priority target, but Inter will have to sell players before they can make another move for the Frenchman.
Inter are looking to move on Brozovic, Milan Skriniar and eve Christian Eriksen in order to make space on their wage bill for Kante.