King has been waiting to leave Bournemouth since last summer and his wait could end on the deadline day of the winter transfer window.
Everton and Fulham have stepped in to approach Bournemouth for the signature of the 29-year-old Norway international in the final hours of the transfer window.
Fulham are also tipped to agree to a relegation release clause if King agrees to join them, but no deal is still in place with Bournemouth.
The two clubs have continued to hold talks with the Championship outfit, but neither are yet to achieve an agreement over a fee.
King is out of contract in the summer and theoretically, he should be available for a small fee.
But for the moment, Bournemouth are yet to give their nod to either of the clubs to secure a deal for King.
The striker’s wage demands are also expected to be a major hurdle with Southampton pulling out of negotiations earlier today due to it.
With only a few hours left in the window, King is again running out of time to secure a move away from Dean Court.