Costa, 28, is currently residing in Brazil and is refusing to return to Premier League champions' training complex in Cobham after Conte informed him via text message that he has no part in his plans for the current campaign.
The fiery Spain international was included in Chelsea's Premier League squad, but his omission from Champions League matters suggests that a winter move is a distinct possibility. Recent reports claimed that Atletico Madrid had agreed a €45m (£41m) deal for Costa, but a mooted move failed to materialise.
Due to his lack of involvement in Europe's premier club competition, Costa will not be cup-tied for the latter stages of the tournament and would thus be available to figure for Atletico - or indeed another club - in the knockout rounds if he completes a January move away. Chelsea would also be able to command a higher fee for the striking hero turned villain, who was linked with a short-term loan move to Everton during the final stages of the transfer window.
Conte will still be able to call upon forwards Michy Batshuayi and record signing Alvaro Morata in the Champions League, while deadline day signings Davide Zappacosta, Danny Drinkwater have also been included. Fellow summer recruits Antonio Rudiger and Tiemoue Bakayoko have predictably been selected, too. Lesser-known starlets Jake Clarke-Salter, Kenedy, Kyle Scott and Charly Musonda have also been selected by Conte.
Chelsea are not the only English team to leave a senior forward out of the group stage reckoning; Tottenham boss Mauricio Pochettino has decided to omit misfiring Dutch striker Vincent Janssen from his Champions League squad, along with long-term injury victim Erik Lamela.
Janssen, 23, rejected a move to Brighton and Hove Albion in order to stay and fight for a place in the Spurs starting line-up, but that decision seems to have already backfired with Fernando Llorente and Harry Kane far ahead of him in Pochettino's pecking order.