Published: 2019-06-25 02:52:15 BdST
Roy, who smashed 153 against Bangladesh earlier in the tournament, was injured in the win over West Indies 10 days ago and has missed games against Afghanistan and Sri Lanka.
A second scan on Monday morning showed Roy's injury was much improved, boosting hopes he will be fit to play in the match against India at Edgbaston on Sunday.
"It's all positive news, he won't be fit tomorrow but we will monitor his progress this week. We will see how it goes," England captain Eoin Morgan told a news conference on Monday.
"Of course he's a big loss, it's Jason Roy. He's an outstanding performer who epitomises the way we play as a group."
James Vince is likely to continue to deputise but has struggled to deliver solid starts at the top of the order with scores of 26 and 14 in England's previous two matches.
The loss to Sri Lanka was England's second league stage defeat and the pre-tournament favourites currently occupy the fourth and final semi-final spot in the standings.
However, their chances of progressing are made significantly more difficult by the fact their three remaining games are against Australia, India and New Zealand, arguably their three biggest rivals for the title.
Morgan does not believe Tuesday's match is a "must-win" and has backed the players to deliver under pressure.
"We don't need to win every game to get to the semi-finals," he added.