Steve Bruce revealed that the 24-year-old's move to the KC Stadium broke down on Monday night.
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"There has been a bit of a problem with his medical, which is the worst scenario for everybody concerned," Bruce told talkSPORT.
"It's an awful situation we find ourselves in but the medical is not great so it looks as if it is a non-starter at the moment. I think he is surprised because he has not missed many games over the last couple of years.
"It is a blow for him and a blow for us but these medicals are so stringent and obviously he has got a problem."
Austin would have been Hull's sixth signing following their promotion to the top flight after Allan McGregor joined George Boyd, Maynor Figueroa, Curtis Davies and Ahmed Elmohamady at the KC Stadium.