Canada coach John Herdman said Davies was "still building toward top speed. But he hasn't hit that top speed yet."
"When you have hamstring injuries, there's always the key moment," Herdman said Saturday. "That's when the hamstring is pushed, pushed to its limits.
"We've got to get this one right because it could be a long tournament for Canada. And that's the last thing I want is for Alphonso to miss this."
After arriving in Qatar in recent days, Herdman said that Davies couldn't wait to take the field for Canada in what is their first World Cup since 1986.
"He's really excited," Herdman added. "Who wouldn't be when you see an 80-foot poster of yourself when you are driving into your hotel."
Eustaquio has an unspecified injury, and Borjan complained of abdominal pain in Canada's 2-1 victory over Japan on Thursday in a friendly in Dubai. Borjan was held out of training on Saturday.
"That's the life of a coach," Herdman said. "I mean, it's bleak on one side but it's opportunity on the other."
Added midfielder Samuel Piette: "We played multiple games without Alphonso Davies during qualifying and we did really well. We don't want to miss these guys. We want these guys on the pitch. But at the same time, it's who's ready to answer the call.
Canada face an arduous task to get out of Group F, going up against No. 2 ranked Belgium as well as 2018 World Cup runners-up Croatia. Piette, though, insists the team have no fear after finishing top of CONCACAF World Cup qualifying to earn their passage to Qatar.
"We want to shock the world and show that Canada is a serious football country, and a serious team," Piette said. "And hopefully we start on the right foot against Belgium."
Information from the Associated Press was used in this report.