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.
1. West Ham
The Hammers are considered favourites at 6/4 to land their man
2. Everton
The impressive Toffees could well continue their spending spree and are at 2/1 to secure King's services
3. Fulham
Scott Parker wants to boost their fire power and they are 5/1 to bring King to West London
4. Tottenham
Spurs were heavily linked with the Bournemouth man but their odds have since drifted to 12/1
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