His older brother Mischa has told Prime Video that 40 millilitres of liquid and blood were removed from the damaged left knee on Tuesday in London.
He said Alexander will undergo another examination on Wednesday in Monaco to determine whether the injury is severe after all.
"If it's a fracture in the bone or a hairline fracture or whatever, then you have to see how long it lasts. But then the Olympics are in danger," Mischa Zverev said.
The Paris Olympics tournament is July 27-August 4, at Roland Garros where he reached the French Open final last month.
Zverev sustained the injury when he slipped during his third-round match on Saturday. He then lost in five sets against American Taylor Fritz in the next match on Monday, playing with painkillers.
Alexander Zverev grimaces after falling down during his match against Cameron Norrie. (AP PHOTO)
Zverev originally said post-match that he would only be doubtful for next week's ATP clay tournament in his home city of Hamburg.
"I would have to play Hamburg in eight days," Zverev said after his round-of-16 exit to Fritz.
"It's something very painful, but it's not dangerous. And when the pain is gone, it's gone."
The advantage of playing in front of his home crowd in Germany would be to get used to clay again before Paris.
"I have to see how it develops," the world No.4 said of his injury.
But three weeks would be "more than enough time" to get fit for the Olympics.
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