Discussions have taken place with the 6ft 8in forward's parent club Monaco on the best course of action, but, if an operation is required on a hamstring injury, it will almost certainly end his short stay at Goodison Park.
The 23-year-old, who arrived on loan on January 24 with an existing hamstring injury, was withdrawn from the starting line-up at Chelsea on Saturday after reporting a problem with his other leg during the pre-match warm-up.
"It is important we are working together with Monaco and what we need to get right is the player gets the perfect treatment: when I say the perfect treatment, this is not a straightforward injury," Everton manager Roberto Martinez said.
"Lacina had a previous injury a few months back but he was fully fit and without fatigue - because obviously in the warm-up you don't incur any fatigue - (so) that injury is a bit of a worry.
"The injury can be solved by conservative treatment or it can involve surgery - that is a massive decision.
"Depending on what route we are going down is going to have certain consequences.
"It could mean Lacina could play for us again or if he can't - it's a bit too early.
"You get to a point where if it is only going to be a matter of three or four weeks we want Lacina to be here until the end.
"If it is going to be any longer than two or three months then the loan period is over."
Traore has featured in just one match, scoring and playing 61 minutes against Swansea in the FA Cup on February 16.
Everton have an agreement with Barcelona over their on-loan forward Gerard Deulofeu which states the more matches he plays the lower the loan fee will be, but Martinez said it was not possible to say at this stage what the financial situation was with Traore.
"At the moment it is too early to have a final answer for that because obviously we don't know how long he will be out for," he added.
"It is important we work together with Monaco and get the best possible treatment for the short and long term."
There was more disappointing news on the injury front with a hamstring concern ruling out captain Phil Jagielka for a couple of weeks, meaning he will also not be available for England's friendly against Denmark on Wednesday.
However, another on-loan striker, Romelu Lukaku, is set to return at home to West Ham at the weekend after being sidelined for a month with an ankle injury.
"This has been the most demanding season personally in his career," Martinez said of the Belgium international.
"The injury has come at a good moment as it has refreshed him and he is desperate now - if you see him in training you see the Romelu we saw in the first week of training."
Lukaku is due to return to parent club Chelsea at the end of the season but Martinez said there had been no discussions about keeping the striker for the longer term.
"The only thing we are interested in is Romelu's development, and that is where we get the rewards of an outstanding footballer who an make a difference on the front line," the Toffees boss said.
"The final 10 weeks is where you can control the small margins and he is in the perfect frame of mind to be as good as he can be."