The Norwegian netted 48 goals in 161 appearances in the top flight and with the domestic transfer window open until October 16, the race to sign the 28-year-old is well and truly on.
Scroll down and click through to see who the bookies think is favourite to land their target, according to Sky Bet.
5. Aston Villa
Villa may have put seven past the champs but Dean Smith remains in the market for another striker. They are 14/1
6. West Brom
King's goals and experience would be very handy for the newly promoted Baggies. Bilic's boys are at 20/1
7. Man United
The Reds almost sealed the deal for King but they have since brought in Cavani. They are drifting at 28/1
8. Brighton
The Seagulls could ruffle a few feathers if they land the striker but they are outsiders at 33/1