Spain striker Costa scored 20 goals in 35 league appearances in Chelsea’s title-winning campaign last season.
But Conte let the 28-year-old know he is not needed at Stamford Bridge any longer with Romelu Lukaku reportedly replacing him in a £100m deal.
Costa says: “Conte has sent me a message to tell me I am not in his plans for Chelsea.
“My relationship with the coach has been bad this season. It’s a shame, but it’s clear that the coach does not count on me and he does not want me there.”