The striker is pushing for a return to the La Liga side after three years at Stamford Bridge.
Conte informed the Spain international by text he is not in his plans for next term.
And that has seen their relationship deteriorate further after a troubled year together.
Despite Chelsea’s title success, Conte and Costa clashed during the season.
The situation is not going to be resolved, leaving Chelsea looking to offload the 28-year-old as soon as possible.
Diego Costa wants to leave Chelsea and rejoin Atletico Madrid
Costa, though, has his heart set on going back to Atletico, and talks are ongoing between the teams even with the Spanish side’s transfer ban complicating matters.
Chelsea have allowed Costa to miss the squad’s pre-season tour to the Far East.
And he took to Instagram to demonstrate his love for Atletico and anger with Conte.
Diego Costa posted a live story showing him dancing at a party while wearing an Atletico shirt.
INCLUSO HASTA SE ATREVE A DECIR UN AUPA ATLETI EN EL SEGUNDO 15. VA CIEGUÍSIMO. DIEGO C DESECANDENADO. MI DELANTERO. pic.twitter.com/LJsrlwU33M
— ANNOUNCE DIEGO COSTA (@RauIgarcismo) July 16, 2017
Chelsea predicted team for 2017/18 Sat, July 15, 2017
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Express Sport predicts how the Chelsea squad could look on the opening day of the 2017/18 season
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How might the Chelsea starting XI and bench look in 2017/18?
Chelsea's Diego Costa wrote "give Conte a hug" on his Instagram story
Give Conte a hug
Chelsea team-mate Cesc Fabregas wrote a comment on the video alongisde a laughing emoji saying: “Hahaha”.
In a dig at his current boss, Costa replied: “Give Conte a hug”.
The Chelsea ace is still on holiday in Lagarto in Brazil, and clearly he has no intention of reuniting with the Italian manager.
Costa, Conte, Chelsea and Atletico will all hope they can come to an agreement over a transfer as soon as possible.