The 6ft. 8” Ivorian was expected to complete a loan deal to Upton Park from Monaco – for whom he recently signed from Anzhi Makhachkala – but despite having had a work permit processed by the Londoners a switch to Merseyside has now become a possibility.
Toffees chief Roberto Martinez has made moves to steal the giant striker away from Sam Allardyce, as he looks to bolster his options to keep a top four push on track.
It is understood that the 23-year-old is more open to a switch to Goodison Park, with the prospect of a Champions League qualification campaign more attractive that a relegation scrap.
However, Everton are not willing to commit until they know the extent of his injury problems.
Traore is currently out of action with damaged hamstring, and Martinez is not keen to push through a deal if the player is unlikely to be able to feature regularly between now and the end of the season.
Monaco themselves are in favour of a loan deal to Everton, with the in-form side having demonstrated their ability to get the best out of young players with Romelu Lukaku.