The Serie A giants have already failed with a bid to sign Kante in the ongoing window, but they are far away from giving up on taking him to Italy.
But Inter are aware that they will need to sell players before they can table a bid that could convince Chelsea to sell the Frenchman in the final days of the transfer window.
Skriniar is one of their top players the club are trying to move on and they are in talks to sell the defender to Tottenham for a fee of €60m.
But that would not be enough to sign Kante as they would need to replace Skriniar and, according to Italian daily Gazzetta dello Sport, Inter will have to conduct another big sale to get their hands on the Chelsea star.
Chelsea are only prepared to sell him if they receive a fee of around €50m and Kante is also likely to command big wages if he agrees to join.
Inter need to raise more funds from the market and free up their wage by moving on another high earlier in the final days of the transfer window.
It has been claimed that Inter are looking to sell either Marcelo Brozovic or Christian Eriksen to make space for Kante.
The 29-year-old is the man Antonio Conte wants and Inter are doing everything to possible to raise the funds that would enable them to sign the Frenchman.