The Chelsea striker was expected to be Pearce's first-choice striker during the Games but was taken ill with viral meningitis earlier this month, before being recently cleared by doctors.
The 22-year-old has resumed light training at Chelsea's Cobham training base, but the Team GB coach wants to be sure that he is fully fit before next Wednesday, the final deadline to make changes to his squad.
Sturridge played no part in the squad's training camp in Spain, and missed the side's friendly defeat to Mexico, but is now spending time in the Olympic village.
"There were doubts but he's joined up today and our fitness people are looking at him," said Pearce.
"The Chelsea medical people are happy with where he is but this week will be important for him. I've got to be 100 per cent sure in my own mind that Daniel is ready to go and fit enough to see out a tournament.
The squad will now return to a northern training base, ahead of Friday's friendly in Middlesbrough against favourites Brazil, and their tournament opener against Senegal at Old Trafford.