Star players Nathan Ake and Callum Wilson have already left the Vitality Stadium following the Cherries’ relegation to the Championship, joining Manchester City and Newcastle United, respectively.
Now 28-year-old striker King looks set to be the next in line to move away from the club, with Bournemouth prepared to sell the player for the right price.
King has entered the final year of his contract and the Cherries prefer to cash in on him than lose him on a free transfer, having already lost Ryan Fraser in that manner.
The Norway international has been linked with a number of Premier League clubs, with Aston Villa and Fulham keen to rope him in.
The Villans are said to have considered a £16m deal for King but it could take more to turn Bournemouth’s head.
King will be hopeful that the Cherries lower their demands and let him seal a move back to the Premier League soon.
There have been suggestions that the Norwegian is keen to join Manchester United, who had a bid for him rejected in January, but it remains to be seen if Ole Gunnar Solskjaer returns for his countryman.