The 22-year-old Chelsea forward fell ill last weekend with viral meningitis - typically considered to be 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 Spain.
"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 Spain when we do our prep there and all being well we'll pick him up when we fly back into the Olympic Village Monday week. We will assess him at that time.
"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. July 25 is that latest we can make that decision.
"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 Loughborough University on Sunday, where the squad undertook their first training session together. The team's first match comes when they play Brazil in a warm-up at Middlesbrough on July 20 - a game Pearce knows will show how good his side can truly be.
"Brazil is probably the ultimate acid test," he said. "I think Brazil and Spain will be the two favourites for this competition.
"Looking through the Brazil squad, you can see the magnitude of the players and how seriously they take the Olympics, as all 16 teams fighting to try and achieve gold will certainly be. 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."