One of the world’s most in-form batsmen when fit, Clarke, 32, is yet to train after treatment in London last week and missed both of Australia’s warm-up games.
“He is making steady progress but is yet to return to training,” Australia’s team physiotherapist Alex Kountouris said.
The Allan Border medalist is also a question mark for the second game against New Zealand.
“How he responds to the ongoing treatment will determine his availability for the match against New Zealand next Wednesday,” Kountouris added.
Coach Mickey Arthur has said this week he remain confident his captain will be fit for the Ashes starting at Trent Bridge, Nottingham, on July 10.
“I am concerned but confident we will have him firing somewhere in this tournament for us and then into the Ashes,” he told BBC.
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