The Switzerland international has been out of action since Arsenal's 3-1 victory over Tottenham Hotspur in September.
Xhaka sustained the problem in an awkward collision with Tottenham forward Lucas Moura in the build-up to Heung-Min Son's consolation goal.
Summer signing Albert Sambi Lokonga has often played alongside Thomas Partey in Arsenal's midfield in place of Xhaka.
The 29-year-old's presence in the Gunners' midfield, though, was missed during their 4-0 defeat to Liverpool at Anfield, ending a 10-game unbeaten run.
But Arteta remains hopeful that Xhaka can make a swift return to the side ahead of the festive period.
"Hopefully he will be a little bit sooner than expected," said Arteta.
"He is training and pushing himself and all the staff so hard like he always does.
"He is in a good place, he is evolving well and hopefully we can have him a little bit earlier. It is still a bit early to decide."
The former Borussia Monchengladbach star's return comes at a perfect time with Partey and Mohamed Elneny set to be involved in the Africa Cup of Nations.