Sky Sports News HQ reported the talks with the Rossoneri:
Meanwhile, per Eduardo Fdez-Abascal of AS, Conte is hoping to move Costa on this summer, but the striker's first-choice destination is unlikely to happen:
Costa's former club Atletico Madrid are banned from registering new players until January, but Milan are seemingly an option:
Costa was back to his best last season as he netted 22 times and laid on eight assists to help fire Chelsea to the Premier League title.
However, it appears the Italian wants to take the team in a different direction and replace Costa with a striker of his own choosing.
Despite the Spain forward's form, football writer Andrew Gaffney was not surprised:
Tancredi Palmeri of beIN Sports also believes Conte had cause to move Costa on:
AC Milan may not be the giants of European football they once were, but they're illustrious enough that they may still hold appeal to Costa, and a signing like him would show real ambition for the Italian club.
The Rossoneri have need of more firepower after mustering just 57 goals in Serie A last season, with Carlos Bacca the only player to reach double figures in the league with 13.
They'll need more than just Costa to turn them back into title contenders, but he would certainly be a step in the right direction.