England skipper Gerrard fit to face Italy
Gerrard struggled through training on Monday, and did not take part in exercises with the rest of the squad.
However, Hodgson expects to have his skipper available for Saturday's FIFA World Cup opener against Cesare Prandelli's side, while Alex Oxlade-Chamberlain is also approaching full fitness.
The Arsenal man tweaked ligaments in his right knee during England's 2-2 draw with Ecuador in Miami last week, but was back in light training on Tuesday.
Oxlade-Chamberlain will not face the Italians, but Hodgson remains hopeful of having the pacey midfielder back for England's second Group D game against Uruguay next Thursday.
When quizzed on Gerrard's fitness, Hodgson replied bluntly: "There's absolutely nothing wrong with him."
He added on Oxlade-Chamberlain: "I think he did very well. Admittedly it's in straight lines but it's very positive that he can run. We'll be stepping up his programme.
"Certainly that's what we are hoping for (Uruguay) but if you really wanted an extremely truthful report, you'd have to go to the medics. They are hoping by the second game, he will be fit, yeah."