The Arsenal midfielder suffered an injury to a medial ligament in his knee during the 2-2 draw with Ecuador in Miami on Wednesday night which will keep him out for between 10 and 21 days.
If Oxlade-Chamberlain is sidelined for the full three weeks it will mean he will miss all three of England's group games.
Hodgson can select a replacement until 24 hours before the first game kicks off, giving the England manager until 11pm on Friday June 13 to make a decision.
"There are no changes, he's been working with the physios and we're monitoring him," said Hodgson, who will also be without the suspended Raheem Sterling for Saturday night's final warm-up game, against Honduras in Miami.
"We're keeping our fingers crossed he can take part in this World Cup for us.
"It won't be a decision we make before we go, it will be at the very last moment which on my understanding is 24 hours before our first game.
"They're working very hard with him and he's working hard so let's see. Let's hope it's not that serious and there won't be a question of him leaving us.
"It was a blow for him because he was playing so well and having a dominant effect but he's a positive boy and his mood is good and our mood towards him is good."
Hodgson has midfielders Michael Carrick and Tom Cleverley on his standby list and another option would be to call up Liverpool full-back John Flanagan to free up James Milner, who played in defence on Wednesday night, into midfield.
The England coach is confident he has suitable options to replace Oxlade-Chamberlain but is not considering them at this point.
"It won't be difficult to come up with the right solution," he said. "But there's no need for us to do that yet."
Hodgson was speaking at a press conference in Miami, where a Football Association delegation, including Sir Trevor Brooking, will attend an event on Friday night to mark the 70th anniversary of the D-Day landings.