The former has been stepping up his work on the training field over recent days and, according to Hodgson, there are no worries about the latter.
"We did a training session (yesterday) where the players who didn't play on Saturday (against Honduras) trained, and some of the others did a warm-down session," he said.
"Steven did some extra work at the end of that training session. There's nothing wrong with him and I don't understand that story at all."
On Oxlade-Chamberlain he said: "He's done very well and will work on his training programme during the course of the week."
With the Italy game now four days away, the hype is increasing but Hodgson will not be giving away any team secrets.
"I don't intend on giving too much away, other than what I've said on that - that it's good to have options and choices," he said.
Hodgson has taken a young squad to Brazil and added: "It's very exciting. We have a lot of potential but before we build people up too much and say how good they are, let's see some performances.
"But I must advise some kind of caution because, as you know, the players haven't had much chance in an England shirt to show that potential can be realised.
"I personally think it will be but, before we build people up too much and say how wonderful these young players are, let's see some very good performances in an England shirt first.
"We know they can do it, we believe they can do it, but let's just calm ourselves down a little bit before we start saying that we have world-beaters in our squad.
"To be a world-beater, you've got to put your international shirt on and play very well.
"I think we have more options [than at Euro 2012]. I think we certainly have more athleticism, we have more pace, more mobility. We have a lot of technical players.
"I certainly am not trying in any way to play down the fact the future looks quite bright and there are some very, very interesting times ahead for us, I'm sure."
- Sports & Recreation
- Alex Oxlade-Chamberlain