Despite vowing to be "ready" against Uruguay, Salah missed training with his compatriots at the weekend and was only able to carry out limited drills on Monday.
"We're keeping an eye on the situation day by day," Egypt managing director Ehab Lehita told Sky Sports News.
"We have been following the case since his injury in the final of Champions League. Mohamed trained in Cairo, trained yesterday and is training today. We are watching the situation closely with the doctor.
"He has daily treatment sessions on his shoulder. He trains indoors as well in the gym, and today he trained on the pitch. He is gradually getting better. However, I cannot confirm today that he will play in the first match. All I can say is that we hope he will play in this match."
Following the Uruguay opener, Egypt face hosts Russia on June 19 before rounding off their Group A campaign against Saudi Arabia six days later.