Oxlade-Chamberlain got injured in the Three Lions' 2-2 draw with Ecuador in a friendly at Sun Life Stadium in Miami.
The 20-year-old is therefore a doubt to play in his country's group games at the Fifa spectacle, but he could still travel with the squad to Brazil on Saturday night.
"We will do everything in our power to keep him (in the squad). Our medical team are optimistic and he is optimistic," Hodgson said at a Vauxhall-sponsored England fans' forum.
"We can't say how long for certain it will take him to recover but obviously he will get very extensive treatment.
"We have the right to replace him if we want to up to 24 hours before the first game.
"We will do everything we can to keep him with us because: a) we would we like to think we might go beyond the group stage although we can't guarantee it, we are certainly planning for it.
"And b) he played so well yesterday. He was undoubtedly our best player in the time he played and it would be a major blow if we lose him. "
England will open their World Cup campaign against Italy on 14 June.