He joined Liverpool from the Gunners for £34million four years ago, but has struggled to earn a starting role since suffering a cruciate ligament rupture in 2018.
Oxlade-Chamberlain returned from that blow to help Liverpool win the Champions League in 2019 after almost a year out.
But he has since had several more setbacks, including a knee injury which sidelined him for three-and-a-half months last season.
He will have hoped for more action this term following the departure of Gini Wijnaldum.
But after lining up for the opening game of the Premier League season he has made just one further start, in the Carabao Cup, as well as three appearances from the bench.
And Arteta could be watching closely to see whether Oxlade-Chamberlain is given a chance to impress at Vicarage Road.