Gunners boss Arsene Wenger believes Oxlade-Chamberlain will be a central midfielder long-term.
"As a young player trying to establish himself, he will have to play anywhere the opportunity exists," said Hodgson.
"If I was to say he is a central midfield player and that is where he needs to play, he faces incredible competition. I think he will be quite happy to do the job where we can use him. I know from Arsene from a conversation we had in private that in the long term the centre of midfield will be a good position for him. There is no doubt his energy and ability to turn on the ball helped us."