Rudi Garcia's side return to the competition for the first time in three years after finishing second in Serie A last season.
Saturday's 1-0 success over Empoli means that the club sit second in the table, with six points from two games.
CSKA currently lie fourth in the Russian Premier League after five wins from their opening seven fixtures.
Leonid Slutski's team lost all three away games in last season's group stage to Manchester City, Bayern Munich and Viktoria Plzen.
Garcia will be without influential midfielder Daniele De Rossi, who is serving a one-match European ban.
CSKA Moscow: WLLWW
Possible starting lineups
Roma: De Sanctis; Manolas, Castan, Maicon, Cole; De Rossi, Nainggolan, Pjanic, Florenzi; Ljajic, Destro
CSKA Moscow: Akinfeev; Nababkin, Ignashevich, Berezutski, Fernandes; Natcho, Eremenko; Milanov, Doumbia, Tosic; Musa
Sports Mole says 2-1