Kante, 29, could be sold by Chelsea this summer after their huge spending spree.
Antonio Conte knows the French international from his time in charge at Chelsea and has reportedly made Kante his number one midfield target.
TMW claims that Inter are working on a paid loan deal for Kante with an obligation to buy.
The English club are resisting at the moment and the next two weeks could be important for Kante’s future.
Kante has been one of the most impressive Premier League midfielders since starring in Leicester’s title-winning side of 2015-16.
Chelsea paid £32m to sign him and he went on to become an important cog in their system.
However, he was hampered by injuries last season and was limited to 20 league starts.
During his time at Chelsea, Kante has won the Premier League, FA Cup and Europa League.
At international level, he was part of the France squad that won the 2018 FIFA World Cup.