The former Gunners midfielder has been training with the club for over a month after leaving Besiktas over the summer.
Oxlade-Chamberlain was working with the U21s before being added to Arteta's senior squad last week.
Asked about signing the now 32 year-old midfielder, Arteta said on Monday: "We explore every option."
The Gunners are in need of a new midfielder after news that Mikel Merino's foot surgery could see him ruled out for the remainder of the season.
Arteta also said before Monday night's transfer deadline: "When you lose a big player like this in the squad with four months to go and all the competitions to play for, you need to look.
"And we need to do everything that we possibly can do to see if we have a player that is available, and if we don’t, we keep what we have."