The France international has not featured sustaining the injury in Arsenal's 2-2 draw with Everton in August, having undergone surgery later that month.
While recent arrival Danny Welbeck has helped to make up for Giroud's absence with four goals in all competitions, Wenger will be keen for Arsenal's top scorer from last season to make a speedy return.
Giroud was initially expected to return to action towards the end of December, but Wenger has been buoyed by the former Montpellier man's progress.
"Olivier Giroud is recovering very well," the Arsenal manager told beIN Sports.
"I believe he is ahead of schedule in terms of rehabilitation. The operation went perfectly."
Giroud scored 22 goals in all competitions for Arsenal last term and lifted the FA Cup - his first piece of silverware with the club.
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