The 28-year-old has been absent without leave since the start of the summer amid rumours of a move back to Atletico Madrid.
Costa claimed manager Antonio Conte informed him via text message that he was surplus to requirements at Stamford Bridge in June.
His falling out with the club escalated further last month after he accused them of treating him like a "criminal" in a newspaper interview and revealed that he had been fined for missing training.
Nevertheless, the forward was named in Chelsea's squad for the Premier League this season suggesting there may at least be some way back into the first-team.
But the omission from the Champions League squad throws his future into further doubt.
Each club must submit a squad with a maximum of 25 players - Chelsea only named 21 players in their squad on Monday afternoon.
Among those named must be a minimum of two goalkeepers and eight "locally-trained players" - i.e. players who spent at least three years between the ages of 15 and 21 on the club's books or on the books of another club in the same country.
An unlimited number of players can also be registered on a 'B list' if they were born in 1996 or later and have been eligible to play for their club for an uninterrupted period of two years since their 15th birthday.
Chelsea's 'B list' players include Andreas Christensen, Jake Clarke-Salter and Kyle Scott.
The club can swap up to three players for the knockout stages in January.
Chelsea squad for Champions League group stage: Willy Caballero, Thibaut Courtois, Eduardo, Antonio Rudiger, Marcos Alonso, Davide Zappacosta, Gary Cahill, Andreas Christensen*, Cesar Azpilicueta, David Luiz, Jake Clarke-Salter*, Cesc Fabregas, Danny Drinkwater, N'Golo Kante, Eden Hazard, Pedro, Tiemoue Bakayoko, Victor Moses, Kenedy, Charly Musonda, Willian, Kyle Scott*, Alvaro Morata, Michy Batshuayi