"He's fit for the game. Luckily we don't have any injury concerns," Hodgson said.
Walcott came on with England trailing 2-1, scored the equaliser and set up Danny Welbeck's winning goal.
He is in contention to replace James Milner, who has been largely disappointing in England's opening two matches.
Walcott travelled to England's training ground ahead of his team-mates on Monday as he attempted to prove his fitness.
Walcott left the team hotel on Monday in a car, which is understood to have been headed for the Hutnik Stadium, while the rest of the squad's outfield players boarded the team bus.
He said: "It's become a very difficult choice because both have done so well both in friendly matches before we came to the tournament, and the tournament itself.
"So they've given me the classic manager's headache but it's the headache we all want because it's a case of players who are in form and playing well and competing for a place.
"But I have made it clear that Wayne Rooney will start so the decision has to be made."
Hodgson's men were forced to conduct their final session before Tuesday's game in Krakow rather than at the Donbass Arena, with the stadium's pitch having taken a battering during the thunderstorm that briefly called a halt to France's 2-0 win over Ukraine on Friday.
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