|2/1||England are 2/1 with William Hill to beat Italy in their opening World Cup match|
The Arsenal winger suffered knee medial ligament damage against Ecuador on Wednesday, but the injury is not quite as bad as first feared.
The 20-year-old wasn't fit enough to take his place in the Three Lions' matchday squad to play Honduras, but he will be ready to head to South America on Sunday.
Speaking to ITV, Hodgson declared: "Oxlade-Chamberlain is making good progress, I think he'll make the tournament for sure.
"We'll be prepared. It's time for the real thing next week. It couldn't have gone much better this week."
Hodgson's side were left frustrated by the Central American outfit after they put in a number of bruising challenges that eventually led to the sending off of Brayan Beckeles.
And the former Switzerland coach admitted that the fixture in Miami had been one of the more frustrating of his management career.
"They were quite physical and it was a real stop-start game. It was one of the most frustrating games I've been involved in in a long time.
"It was a giant attack versus defence but we unfortunately didn't take the chances. Our tempo and effort to score in the second half was commendable but it was a frustrating game and one I'll be quick to forget."