The Leicester forward limped off nursing a knee problem during England's 22-9 tournament warm-up loss to France in Marseille 11 days ago.
England's 30-man World Cup squad assembled at Twickenham on Wednesday, where they held a light training session and although Corry did not take part, England head coach Brian Ashton delivered an upbeat bulletin.
Ashton said: "Martin didn't train today, but he is continuing his rehab from a left knee injury.
"We believe he will be fit and in contention for a place in the 22 for our first pool match."
While Corry missed the session, scrum-half Peter Richards moved to allay fears about his fitness.
The London Irish number nine missed all three warm-up games because of a lower back injury which prompted Ashton to summon uncapped Sale Sharks scrum-half Richard Wigglesworth as precautionary cover.
Ashton added: "I am pleased to say that Pete Richards has done everything we have asked of him in the last 10 days.
"He passed a fitness test on Monday, and rested yesterday.
"He received a further assessment from the England medical team this morning, and took a full part in training along with (Leicester hooker) George Chuter, who withdrew from the Test match in Marseille with a knee injury."
England's World Cup skipper Phil Vickery is also believed to be on course to make the opening game after being carried off concussed in Marseille.
England are now based in London until Monday, when they fly to Paris before moving on to their Versailles training base.