The 22-year-old Chelsea forward fell ill last weekend with viral meningitis - what is typically considered a mild strain of the disease.
Earlier this week Sturridge revealed he is confident of recovering in time for the Games, although Pearce will not be taking him on next week's pre-Games camp in
"Doctors had a look at him last week, visited him and basically he will stay here," Pearce told Press Association Sport.
"He won't come to
"The good thing is we probably have a couple of weeks to make a decision on his fitness.
"If he is fully fit, he will stay with us. If we think there are any doubts in any shape or form, we'll call someone else to replace him.
"We still have a few weeks in respect to that, but the important thing is probably once we get him on the training pitch to look at him and see how he is and how much this illness has affected him."
Sturridge was absent from Team GB's Preparation Camp at
The team's first match comes when it plays
"Looking through the
"It will be a fantastic friendly for us and it will lead us nicely into the tournament and I think it will showcase to everybody in the tournament the standard of football in it."