The Ivorian moved to Goodison Park on loan from Monaco in January and scored on his debut in the 3-1 FA Cup fifth-round win over Swansea City.
However, he then suffered a hamstring injury during the warm-up ahead of the Merseysiders' 1-0 defeat at Chelsea on February 22.
Everton boss Roberto Martinez subsequently said that Traore's loan deal would be terminated if he needed an operation, but the Spaniard revealed on Tuesday that he hopes to have the 23-year-old available again before the end of the season.
"We've seen the specialists and it's not going to be surgery, which is fantastic news," the former Wigan boss told reporters.
"We're expecting between six and eight weeks to be the period he needs to be recovering, but we're all very positive.
"It's fantastic news that he doesn't need surgery, as that means he's going to be available for the end of the season."
Martinez also refused to rule out captain Phil Jagielka for Saturday's FA Cup quarter-final at Arsenal, although the defender remains a major doubt due to a hamstring problem of his own.