The Frenchman sustained the injury in a 2-2 Premier League draw with Everton in August, but is in contention for a return on Saturday - a month earlier than had been anticipated.
Captain Mikel Arteta could also feature this weekend following a hamstring problem, but manager Arsene Wenger knows he must be cautious in reintroducing the pair.
"Giroud and Arteta are both available," he said. "It's just a question of how ready they are. But they are available.
"[Giroud] is three or four weeks ahead of schedule.
"Originally we planned to have him back for competition at the beginning of next year. So he's one month ahead."
Asked whether his side had relied heavily on Danny Welbeck in the absence of Giroud, Wenger said: "Yes, and on [Alexis] Sanchez as well. But we have Giroud back, we have [Theo] Walcott back.
"Slowly they will integrate into the team again and give us different options."
Arsenal remain without the services of Mesut Ozil, who Wenger does not expect to return from a knee injury until the new year, but Laurent Koscielny (Achilles) and Matthieu Debuchy (ankle) are back in training.
"Koscielny and Debuchy are doing well, they are out on the field [working] again," Wenger added. "We have to see now.
"Usually field work is three weeks away from full group training. Then there is fitness.
"It looks straightforward for Debuchy. It's not inflammation, it's just repairing surgery.
"For Koscielny, it depends how well he responds to training. At the moment he looks good."
