The 6ft. 8” striker was believed to be on the verge of sealing a shock loan move from Monaco to the Hammers, with Sam Allardyce’s having successfully applied for a work permit for the Ivorian.
However, the London club have not yet processed all of the paperwork, leaving the door open for rival sides.
Everton are said to be ready to take advantage of this to snap up the giant front-man.
Roberto Martinez is thought to be keen to add another forward to his ranks, and sees Traore as an ideal partner for in-form loanee Romelu Lukaku.
The 23-year-old himself may also be more open to a switch to Goodison Park, with the Toffees battling for Champions League qualification, rather than against the threat of relegation.
Traore only joined Monaco from Anzhi Makhachkala last week in an £8.6m deal, but the French outfit are prepared to send him out on a temporary basis to find his form and fitness ahead of next season.