The 6ft 8ins striker looked set to join West Ham last week, and even had a work permit granted, but Sam Allardyce missed out on Ivory Coast international who now looks to be on his way to Merseyside.
Everton look to have hijacked the deal for Traore and Allardyce admitted earlier this weekend there is nothing they can do to stop the Goodison Park outfit signing the player.
When asked after Saturday's defeat to Newcastle if Traore would be signing for the Upton Park club, he said: "It's unlikely by the sounds of it.
"We're finding it extremely difficult (to bring players in).
"We had a terrible day yesterday (Friday) when I thought a player was signing for us and then I found out he wasn't, but there you go.
"[Any other club] can apply for a work permit like we did.
"They would have to do a separate application."