The 6ft 8in Ivorian, who was originally expected to join West Ham, has moved closer to a temporary switch to Goodison Park, having only signed for Monaco earlier this month
Traore joined the Ligue 1 side from Russian club Anzhi earlier in January and was originally expected to join West Ham.
But the striker turned down the Hammers and is now close to a temporary spell with the top four-chasing Toffees.
Roberto Martinez confirmed Everton had applied for a work permit for Traore following Monday's 1-1 draw with West Brom at the Hawthorns.
The Toffees have been on the lookout for attacking reinforcements, having sanctioned the sale of Nikica Jelavic to Hull City for an undisclosed fee earlier this month and lost Victor Anichebe last summer.
Romelu Lukaku's goals have so far helped Martinez's men sustain a surprise top-four challenge, but the Chelsea loanee has netted just once in his last nine games.