Traore, who joined Everton in the January transfer window but has featured in only one game, suffered a hamstring injury before last week's Premier League match with Chelsea.
He will now see specialists in England and France who will assess the problem before a decision is made on whether he remains on Merseyside.
"We have been working closely with Monaco to ensure we get the best possible treatment on the injury," Martinez said on the club website (www.evertonfc.com).
"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.
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"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 all aiming for," added Martinez.
The Ivorian striker scored after four minutes of his only game at Everton, a 3-1 FA Cup fifth round win over Swansea City.
(Reporting by Toby Davis; editing by Josh Reich)
