Inter coach Antonio Conte has made signing Kante a priority in the current transfer window and the Nerazzurri are doing their best to grant him his wish.
Chelsea have rejected an offer from Inter which included midfielder Marcelo Brozovic, while they have also told the Serie A giants they are not interested in a proposal which includes Eriksen.
Inter signed Eriksen from Tottenham in the January transfer window earlier this year.
Eriksen enjoyed 17 outings in Serie A last term, scoring once and providing two assists, and has another four years to run on his contract in Italy.
Chelsea are not willing to bring him back to England in a deal which sees Kante go the other way, and the Blues have strengthened their attacking midfield options over the course of the window so far.
Inter could come back with another proposal for Kante, as they look to tempt Chelsea into selling.
The Blues are expected to offload fringe players in the coming weeks as they look to bring in cash following a period of substantial spending.
