Former Leeds skipper Austin, 30, was freed by United at the end of last season and has been linked with a number of Championship sides, including the Owls, Ipswich, Middlesbrough, Bolton, Birmingham City and Nottingham Forest.
Following international duties in Jamaica, Austin was keen on resolving his career in the UK, with the Owls reportedly offering the player a return to Yorkshire.
But stringent new rules restricting the number of overseas players in England football look to have blocked a move for Austin.
His agent said: “Rudy has spent the summer playing in the Copa America and then helping Jamaica get to the Gold Cup final.
“He has proved himself as a genuine top Championship performer, there were six big clubs who wanted to sign him.
“But we found out yesterday that the new rules mean they won’t allow him a new work permit, which has been a big disappointment.
“His son was born here, Rudy only had two years to stay before he qualified for citizenship and he really wanted to stay and make a life in Britain.
“But there is nothing we can do about it with these new rules. It’s just a shame he has been caught up in them.”
It is understood Austin has other offers to play in Turkey and the USA, although his preferred choice is to remain in the UK.
Austin joined Leeds for a six-figure fee from Norwegian outfit SK Brann in the summer of 2012 under Neil Warnock.