The Midland's outfit are reportedly in financial trouble and need to sell players to keep the books balanced, it is believed that King is one of the players who have been told to look for a new club.
King, although 32, is Birmingham's top scorer this season and he has hit 30 for the club since joining from Coventry City in 2011.
He currently has 18 months left to run on his current contract but Sky Sports say that he can leave on a free transfer.
Wigan, Cardiff and Nottingham Forest are also being linked.