The winger featured in the position for Arsenal against Manchester United last weekend.
The 23-year-old has played in a number of positions since breaking through at Southampton, featuring as a right winger, left winger, number 10 and central midfielder over the years.
Saturday afternoon saw him take up a new role as Arsene Wenger used him to replace Carl Jenkinson at right-back in the game against Manchester United.
It proved to be a successful choice, with the England man racing clear to set up Olivier Giroud’s equaliser late on.
And Carragher believes he could look at moving into the position full-time later on, as Antonio Valencia has done at Old Trafford.
"Jamie Redknapp was quite critical of Marcus Rashford the other day,” he told Sky Sports.
"[But] I've got a little bit more sympathy for him, and the reason why is because yes, Oxlade-Chamberlain has gone to a fullback position.
"And I think maybe going forward that could be a position he could look for. Look at how [Antonio] Valencia has done it for Manchester United.”
Unfortunately for Oxlade-Chamberlain, he is unlikely to be used at right-back by Arsenal any time soon given their strength in that position.
They already have Hector Bellerin there and given he has just signed a brand new long-term deal at the Emirates Stadium,the winger will not be replacing him anytime soon.
Instead, he must focus on getting in the team ahead of the likes of Alex Iwobi, who has somewhat supplanted him over the last year.