The dynamic Surrey opener tore the muscle while fielding in England’s group win over the West Indies and has been ruled out for at least two games including Friday’s match with Sri Lanka at Headingley.
Roy was advised against batting during a brief net practice at Yorkshire’s headquarters on Thursday.
Although he is keen to face arch rivals Australia at Lord’s on Tuesday, an England side bidding to win the World Cup for the first time may well decide against risking Roy given they are already on course to reach the semi-finals.
“I’m working extremely hard. I’ve now got two days off and I’ll have scan in a couple of days to make sure everything is going in the right direction,” Roy told BBC Radio’s Test Match Special during England’s match against Sri Lanka on Friday.
“It’s healing pretty well. It’s all good news. At the moment, I’m still trying to be fit for Australia, and then it’s got to go game by game.
“It can’t be ‘I’ll definitely be back for this game or that game’, it’s something that we have to manage day by day.”
Roy hit a fifty in England’s opening win over South Africa and then struck a commanding 153 in the host nation’s victory over Bangladesh.
“We have the semi-finals and the final and all of that to play for,” he said. “If you look at it game by game, you can get frustrated, but I don’t do that.”