Giroud injured his ankle on August 23 and was not expected to return until January, after all the group fixtures had taken place.
Clubs can only register 25 players on an 'A List' for the Champions League group matches, which must be submitted by September 2 and include eight home-grown players.
Arsenal need just one point from their remaining two games to qualify for the knock-out stages and Giroud could be included for the rest of the competition, with the next squad list due by February 3.
Arsene Wenger's side, who are five points off top spot, host group leaders Borussia Dortmund on Wednesday before finishing with a trip to Galatasaray.
Giroud came off the bench against Manchester United on Saturday and marked his comeback in dramatic style with a stunning late goal in the 2-1 defeat.
Source : PA
Source: PA