England need all hands on deck after back-to-back defeats complicated their semi-finals passage ahead of their last two group assignments against India and New Zealand -- teams they have not beaten in World Cup since 1992.
Roy smashed 153 against Bangladesh but has since sat out with the injury, while replacement James Vince managed 40 in three innings.
"Jason is preparing to play tomorrow," Morgan told reporters at Edgbaston on Saturday.
"Providing he gets through to today's practice and tomorrow morning unscathed, we think that he might be fit to play."
Roy has been crucial to England's rise to the top of one-day rankings and Morgan said he would risk playing the 28-year-old unless it meant long-term injury for the opener.
"Depending on the significance of the risk. If it was going to rule him out long term, absolutely not. If it was going to rule him out for a couple of weeks, yes," he said.
Archer did not bowl on Friday but rolled his arms on Saturday.
"We're going to see how he comes through today. It's the same thing he's been playing with the last three games. So we'll see how he comes through today," Morgan said.
Many saw the team under Morgan as the strongest England side in a World Cup but defeats by Sri Lanka and Australia have intensified pressure on the hosts.
Morgan admitted his team, who had made it a habit to post 300-plus score heading into the tournament, have struggled to adjust to pitches where teams have successfully defended sub-250 totals but refused to blame his team mates.
"I can't fault the commitment or application that the guys have produced in every single game," Morgan said.
"Where we've let ourselves down as a group is adapting to conditions. It's been a bigger challenge in this World Cup than previous bilateral series that we've played.
"So tomorrow's going to be the exact same. We're going to have to adapt to conditions, adapt to playing against a strong side in India."
(Reporting by Amlan Chakraborty in Birmingham; editing by Christian Radnedge)
