The Arsenal winger suffered medial knee ligament damage during Wednesday's friendly against Ecuador, with the Football Association confirming that his condition will be monitored before any final decision will be made.
And Hodgson is hopeful the 20-year-old will, at the very least, be available for the knockout rounds and thus will stay with the travelling party with a view to him being fit for as many matches as possible.
|21/10||England are 21/10 with Paddy Power to win Group D at the 2014 World Cup|
"We will do everything in our power to keep him. Our medical team are optimistic and he is optimistic," he told a fans' forum in Miami.
"We can't say how long for certain it will take him to recover but obviously he will get very extensive treatment.
"We will do everything we can to keep him with us because 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."
The former Southampton starlet impressed against the South American outfit with his direct running, and Hodgson admitted that he was the pick of the Three Lions players in what was a largely experimental side.
"He played so well yesterday [against Ecuador]," he added. "He was undoubtedly our best player in the time he played, and it would be a major blow if we lose him.
"He was back really to his best so all I can do now I suppose is cross my fingers and touch every piece of wood I pass by that it is not serious."
England take on Honduras on Saturday in their final warm-up match before preparing to play Italy in Manaus on June 14 in their opening Group D encounter.