The 22-year-old forward fell ill over the weekend with what is typically considered a mild strain of the disease.
Di Matteo, speaking at his club's Cobham training complex, confirmed Sturridge was still in hospital but suggested he could still play a part in the Games providing his recovery goes well.
"Daniel has viral meningitis, but I spoke to him and he feels better now," said Di Matteo. "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 an hourly basis. We'll see and make a decision with the doctors and if he can join."
Sturridge also remains positive about his prospects of recovering in time for the Games. He said in a statement: "The Chelsea medical team have been closely monitoring everything and they and the doctors and nurses at St Mary's Hospital have been outstanding throughout.
"Thankfully, I am starting to feel a lot better and I am optimistic about being able to make the Olympics. I am fortunate to have received many wishes of support and I want to thank everybody who has sent messages, it is much appreciated."
Stuart Pearce's 18-man Team GB squad is set to meet in Loughborough next weekend and the manager has until 25 July to select a replacement should Sturridge be forced to withdraw.