Barclays Premier League new boys Hull have shelved a move for the striker after he failed a medical.
It came as the Tigers had looked to be closing in on a reported £4.5million deal for the 24-year-old, who scored 28 goals last season, as he underwent checks on Monday night.
No details of the medical have been revealed, although Austin has a history of shoulder problems.
The frontman has now been omitted from Burnley's squad for Tuesday's friendly against League Two side Morecambe at the Globe Arena, although he is expected to link up with his team-mates on their five-day pre-season trip to Ireland which gets underway on Thursday.
Clarets boss Sean Dyche told the club's official website: "Because of the situation, we have given Charlie a day off to spend time with his family and ready his thoughts before he joins us on the trip to Cork."
- Sports & Recreation