King wanted to leave the Cherries last summer after they were relegated from the Premier League and was heavily linked with a number of clubs in the top tier.
West Ham, Fulham and Aston Villa were looking to sign him, but none of the clubs managed to strike a deal with Bournemouth and he stayed at Dean Court.
He is in the final months of his contract with the club and has again been linked with a move to the Premier League in the ongoing transfer window.
West Ham want a striker to replace Sebastien Haller and King is on their radar as a potential option – but the player is not desperate to move.
He is ready to wait until the summer, see out his contract and leave the Cherries on a free transfer.
The 29-year-old recently scored his first goals of the season in the FA Cup and is happy to stay at Bournemouth until the end of the season.
Bournemouth are prepared to listen to offers for him this month but a transfer will depend on clubs coming in with suitable bids in the final two weeks of the transfer window.