Blues manager Roberto Di Matteo told reporters that the 22-year-old forward was on the mend after being struck down with a mild form of the illness over the weekend.
"Daniel has viral meningitis, but I spoke to him and he feels better now," Di Matteo said at Chelsea's Cobham training ground.
"We're going to follow his situation and hopefully he will get well as soon as possible and be able to join Olympics squad.
"He is currently still in hospital but I am optimistic he will recover [in time to play].
"I think it's a question of daily monitoring his health, that's what matters most to him, his family and ourselves.
"We have had a doctor with him since day one and we are being updated on hourly basis. We'll see and make a decision with the doctors and if he can join."
Britain's Olympic football squad is due to convene next weekend and manager Stuart Pearce has until July 25 to choose a replacement if Sturridge is declared unfit.
Meanwhile Di Matteo, who was appointed Chelsea manager on a two-year deal at the end of the season after guiding the club to a Champions League and FA Cup double, had a message of goodwill for his sacked predecessor Andre Villas-Boas, who was appointed by London rival Tottenham on Tuesday.
"I wish him the best of luck. He is a very good manager and coach and I am sure he will be a success," Di Matteo said.
"It doesn't surprise me [that he has been appointed]. I think it's a good choice." – Sapa-AFP