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"I almost lost my eye," Parker said in an interview posted on his website Sunday.
He did not join the rest of France's team Wednesday and will see a specialist in New York when he is cleared to take long-haul flights after July 5.
"I'm seeing a specialist in New York with the hope of being given the all-clear to play in the Olympic Games," Parker said. "Spurs are very worried.
"Anything can happen, including me being out of the Olympics. The decision doesn't belong to me anymore. It's in the hands of the doctor and San Antonio."
Parker said he has been having hallucinations and been unable to leave his hotel room for eight days because of the risk of infection. He also has to apply five different products to his eye every two hours.