The striker is a wanted man and is expected to be on the move from Bournemouth before the end of Friday, with the domestic transfer window due to slam shut.
Bournemouth have turned down a £13m bid for King from West Ham, while Aston Villa are also amongst the clubs to have been linked with the striker.
While Bournemouth are yet to accept an offer for King, the striker has no intention of staying in the Championship, according to Norwegian daily VG.
The Norway international is firmly against playing in the second tier and could apply pressure on the Cherries to sell him before the transfer window shuts.
King is claimed to be open to a move to a number of different clubs, with playing Premier League football his priority.
Bournemouth are looking for in the region of £18m to sell King before the window closes.
The striker has netted 48 goals in the Premier League and wants to add to his tally this season.
