The Spain international is believed to have been informed via text message from manager Antonio Conte that he was no longer wanted at Stamford Bridge.
Costa is understood to be keen on returning to Atletico Madrid, but because the Spanish club cannot register players until January 2018 due to a ban, it has been difficult to get a deal over the line.
AC Milan have also shown interest in the striker, but according to Sky Sport Italia reporter Luca Marchetti, the Serie A giants are not interested in only having the player on a short-term arrangement.
Marchetti told Tutto Mercato Web Radio: "It is not a simple operation for the Chelsea goalscorer because it was promised he would arrive at Atletico Madrid in January and Milan does not want to take him for six months."
Costa scored 20 Premier League goals last season.