The Sun says Austin, 24, had agreed to join Hull for £4.5million until a knee problem showed up in scans at his medical.
After he was left devastated by the news, the Turf Moor club now plan to hand the striker a fresh contract.
The former builder wanted to play in Tuesday's friendly at Morecambe but he will take time off to get over his bitter disappointment.
Manager Sean Dyche said: "He wanted the chance to play in the Premier League. But I've now got a 28-goal centre forward in the fold."