Kilkenny made 21 appearances for the Whites under Gary McAllister this season, but he has not played under Grayson and is attracting attention from a number of clubs.
Doncaster Rovers are also believed to be looking at Kilkenny, though Leeds have not indicated whether he is surplus to requirements at Elland Road.
Kilkenny cost Leeds around £150,000 when he joined the club under Dennis Wise on a three-and-a-half year deal from Birmingham in January 2008.