The 32-year-old, who has scored over 30 goals since he joined Birmingham in 2011 from Midlands rivals Coventry City, is currently top-scorer for the club.
But Birmingham are struggling hugely financially and are understood to have told a number of players that if they find a new club they would be able to leave.
And Sky Sports understands that King could leave on a free transfer, despite having 18 months left on his current deal.
While King is settled at St Andrew's and is happy, a host of clubs have been alerted to the fact he could be available.
Former club Wigan, Norwich, Cardiff, Blackburn, Bolton and Nottingham Forest are thought to be monitoring his situation.
Along with King is it thought that the futures of big names such as Jack Butland, Nathan Redmond, Chris Burke and Nikola Zigic are very much up in the air.