The 30-year old Ivory Coast striker injured his knee in October last year, just three months after joining from Wigan Athletic, which restricted his debut season at Goodison Park to just five Premier League appearances.
Martinez says that the former Levante and PSV Eindhoven ace was on his way back to full fitness but would still be unavailable for at least a month.
"Arouna is training well and is still in his own programme, but he has been working with the team as well,” the Toffees boss told the Liverpool Echo.
"We're very positive about Arouna being able to play some sort of competitive football in the next four to five weeks."
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