The Hammers have been given permission to talk to the player and he should become one of the first signings of the transfer window.
The centre-back, who is 30, is entering the final 12 months of the five-year deal he signed when he joined from Atletico Madrid for £6 million in 2009.
Sam Allardyce confirmed a deal was imminent.
"We've had the OK from Everton and we're talking to his agent at the moment so hopefully that will happen in the next day or so," he said.
West Ham are currently struggling at centre-back with James Tomkins and James Collins both out injured.
Heitinga has been capped 87 times for Holland but has yet to play for Everton this season.