The 22-year-old is understood to have fallen ill over the weekend and been admitted to St Mary's hospital in Paddington for tests.
Sturridge's condition is said to have improved over the last 48 hours, but his place in the 23-man Great Britain football squad for the London Olympics, named on Monday, is clearly in doubt.
Stuart Pearce's squad is set to meet at the Team GB holding camp in Loughborough next weekend, and Football Association medical staff will assess the results of tests before deciding if Sturridge can still play a part.
Pearce has until July 25 to select a replacement should Sturridge be forced to withdraw, with those on the stand-by list believed to include Huddersfield striker Jordan Rhodes.
But immediate concerns revolve around the health of Sturridge, with more details of his condition expected when Chelsea boss Roberto Di Matteo holds a routine pre-season press conference at the club's training ground on Wednesday morning.
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