The standby duo have been told they could be called up at any time though if Oxlade-Chamberlain does not demonstrate sufficient progress in his recovery from the injury to his right knee.
Hodgson has until Friday to decide whether he will replace Oxlade-Chamberlain, and for now he is positive about the midfielder's chances of playing some part in the tournament.
"That is what we are hoping for," he said.
"But there are still a few assessments to be made on him so I wouldn't want to suggest that is a stone-wall certainty."
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