The 30-year-old was widely expected to complete a transfer to Upton Park after the Hammers agreed a deal with the Merseyside club, but the switch has now been abandoned due to the player himself opting against the arrangement.
The news has alerted Alan Pardew, who has moved quickly in a bid to force through a swoop for the versatile enforcer.
It is understood that the Tyne club have made an official offer, and are hopeful of sealing a deal in the coming days.
Pardew has been forced into the January market after losing captain and centre-back Fabricio Coloccini to injury, leaving him short of cover at the back.
Heitinga is said to have no future at Goodison Park, with his current contract set to expire at the end of the season.
The ex-Atletico Madrid man can play at the heart of the defence, at right-back or in a midfield role, which will be a boost for the North East club if they can conclude a swoop.