The Norwegian is keen to move on from Bournemouth after their relegation to the Championship and wants to play in the Premier League this season.
With the transfer window between the Premier League and the EFL still open until 16th October, King is hopeful of securing a move to a top flight club.
West Brom are interested in the striker, but West Ham boss David Moyes is in a good position to sign him in the next week or so.
The Hammers have been in talks with King and his representatives over agreeing on a deal to move to the London Stadium.
The 28-year-old is keen on the move and the deal is now dependent on West Ham agreeing on a fee with Bournemouth.
Moyes bolstered his defensive options with the arrival of Vladimir Coufal from Slavia Prague and also made Tomas Soucek’s loan a permanent deal in the summer.
But following the departures of Felipe Anderson and Grady Diangana, West Ham are short of options in action this season.
King has been identified as a potential recruit and the Hammers are working on a deal.
He has played just 23 minutes as a substitute for Bournemouth this season.
