This comes after the revelation the Blues coach for next season has made the talented Ghanaian midfielder his first target when he takes over.
Now English newspaper the Daily Star is reporting that a deal has already been reached with the Serie A side to sell the Ghanaian player to Chelsea.
It is not certain how much Chelsea would pay to Juventus for Asamoah to complete his move to England but it is rumoured to be around £25m.
The incoming Blues boss has set about drawing up a list of transfer targets ahead of his arrival this summer.
And he could be about to raid former club Juventus too.
Conte signed Ghana international Asamoah in 2012 when he was in charge of the Turin side.
The Italian is up for a reunion with the Ghanaian in London.
Central midfielder Asamoah has scored five goals in his four years with Juve.
Arsenal were linked with the 27-year-old last year.