Hull boss Steve Bruce has made Austin one of his top transfer targets this summer and has been chasing him for several weeks.
A fee had been agreed between the two clubs but Austin has now failed his medical, with a problem with his knee having shown up on scans.
The 24-year-old has established himself as one of the most prolific strikers in the country since being plucked from non-league football by Swindon four years ago, scoring 82 goals in 155 games for Swindon and Burnley.
"Well first and foremost it is totally disappointing for him in particular," Bruce told Sky Sports News.
"We have been working on it for the last three or four weeks behind the scenes but unfortunately he has a bit of a knee problem and with the amount of money at stake in the transfer fee the problem has shown up pretty visibly with the scan and unfortunately that has put a stop to the deal.
"So it is disappointing, very disappointing, and I have to say on behalf of us all particularly disappointing for Charlie the boy.
"It is totally frustrating, but one thing you have got to do and where football is now the sport science and medical department is now bigger than it's ever been and rightly so with the amounts of money that is being thrown about
"But obviously there is a problem there and a problem which we didn't think we could mend quickly and we have decided to put a halt to it.
"I haven't spoken to him this morning. I was with his dad and agent last night and he is obviously disappointed, but I just hope for him the situation doesn't flare up for him and he can go on to still have a very good career.
"It's no secret we need a striker and we possibly need a couple of them and that's been the aim since we finished the season. That is still on the agenda.
"It is always the most difficult to find because everyone is after a striker, but we go back to drawing board.
"We've still got six weeks before we start really and let's hope we can go somewhere else."
Austin has just 12 months remaining on his current deal and, with no indication that he will sign a new deal, Burnley had been forced to try to cash in on him.
The collapse of the transfer has provided Bruce with further frustration in his efforts to add extra firepower to his squad following Hull's promotion to the top flight and he has previously seen a bid for Celtic striker Gary Hooper rejected.
The likes of Swansea's Luke Moore, West Bromwich Albion's Peter Odemwingie and South African forward Katlego Mphela have also been linked with moves to the KC Stadium, and Bruce will now go back to the drawing board.
The Tigers have so far signed Maynor Figueroa, Curtis Davies and Allan McGregor in addition to securing permanent deals for George Boyd and Ahmed Elmohamady.