The Monaco attacker had previously been heavily linked with the Hammers, having only moved to the Ligue 1 giants from Anzhi Makhachkala on January 4.
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“Lacina is a player that we are very interested in," Martinez told reporters after the 1-1 draw with West Brom at the Hawthorns.
“We need to get over that [work permit] hurdle first and then if we can get through that it will be a good addition to the squad.”
Traore joined Monaco from Anzhi Makhachkala earlier this month for £16 million after featuring 39 times for the Russian club.
The 23-year-old will become the fourth player to join Everton on loan this season, with Gerard Deulofeu, Romelu Lukaku and Gareth Barry all joining the club temporarily.
Traore would join Manchester City goalkeeper Costel Pantilimon as the tallest player in the Premier League at 6ft 8.