Sturridge, named in the 18-man Team GB squad by coach Stuart Pearce on Monday, remains in London's St Mary's Hospital after he fell ill at the weekend and was admitted for tests.
"I am starting to feel a lot better and I am optimistic about being able to make the Olympics," the 22-year-old 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."
Chelsea manager Roberto Di Matteo echoed Sturridge's optimism at his first news conference ahead of the new Premier League season which kicks off on Aug. 18.
"Daniel has viral meningitis. I spoke to him and he feels better now. Hopefully he gets well as soon as possible," Di Matteo told reporters.
"He felt unwell over the weekend and was taken to hospital afterwards."
"I think it's difficult to give a time limit (on his recovery) today. We will monitor him on a daily basis.
"The fact he's feeling better is positive. I'm optimistic he'll recover and he'll be able to join the Olympic team."
Pearce's Britain team has already been dealt a blow with Tottenham Hotspur's Wales winger Gareth Bale already out of contention with back and hip complaints.
Sturridge missed out on England's Euro 2012 campaign and is a key member of the squad for Pearce who controversially opted not to select former England captain David Beckham.
The squad will link up ahead of the Games for a training camp next weekend in Loughborough, Leicestershire.
Team GB play Senegal in their first fixture on July 26, before facing United Arab Emirates and Uruguay in Group A.