The striker arrived at Goodison Park on loan from Monaco in the January transfer window and scored in his debut in a 3-1 FA Cup win over Swansea City earlier this month.
However, the Ivorian suffered a hamstring injury in the warm-ups before Saturday's 1-0 defeat against Chelsea, and Monaco and Everton have agreed that Traore should visit experts in both countries as the teams seek a diagnosis.
If he requires surgery, his loan spell may be terminated, although if the injury is less serious he will remain at the Premier League club for the remainder of the campaign.
"We have been working closely with Monaco to ensure we get the best possible treatment on the injury," Everton boss Roberto Martinez told the club's website. "He will now see two specialists next week - one in London and one in Paris. Then we will make the final decision with the parent club. If Lacina will be fit by the end of the season, then we will see him in an Everton shirt again, and that is what we are aiming for."