The Arsenal man suffered knee ligament damage in a 2-2 draw with Ecuador on Wednesday, putting his presence at the competition in doubt.
However, with the 20-year-old working tirelessly to be ready for a Group D opener against Italy on June 14, Hodgson is willing to give Oxlade-Chamberlain every chance to regain fitness.
Hodgson also confirmed he has no plans to replace the former Southampton man before England leave for Brazil.
Asked on Friday about Oxlade-Chamberlain's progress, the England manager explained: "(There have been) no changes, he's been working with the physios over the last couple of days and we'll monitor the situation and keep our fingers crossed.
"It won't be before we go to Brazil, it will be at the very last moment. They're working very hard with him and he's working very hard also.
"(He has been) very positive, it was a major blow because he was playing so well. His mood is good and our mood, with regard to his injury, is good."
Captain Steven Gerrard could return to Hodgson's starting XI for England's final warm-up against Honduras on Saturday, having been rested in midweek.
Gerrard watched as Ross Barkley, Oxlade-Chamberlain and Liverpool team-mate Raheem Sterling impressed against Ecuador - only for the latter two to have their involvement ended prematurely due to injury and a red card respectively.
Ahead of his third World Cup, Gerrard praised the younger members of the squad, but warned against putting too much pressure on them.
Asked who stood out on Wednesday, he said: "Alex of course, I think he was man of the match. There were a lot of positives.
"Ross was brilliant in flashes but I was more impressed with the all-round performance. I'm really happy with where we are.
"Not just with Ross, but it's important we don't put too much pressure on the young lads.
"He's going to be a terrific player but it's important we don't get carried away."
Hodgson expressed pleasure at the way Sterling has reacted to his dismissal in the Ecuador fixture - for a poor challenge on Antonio Valencia just 14 minutes after the forward came off the bench.
"His reaction has been excellent, he's not going to lose anything in terms of fitness so the dilemma is there's more than 11 players capable (of starting against Italy).
"Raheem Sterling's sending off against Ecuador won't affect his chances of starting against Italy."
