The £5million Ivory Coast striker hasn't played in over a year after suffering a serious knee cartilage injury against Hull on October 19, 2013.
Martinez said: "I expect him to be fully match-fit by January. He'll play in 11-a-sides behind closed doors next week.
"Arouna is in the same boat as Bryan (Oviedo) but the only thing with him is that we are being careful we don't overload him with work.
"As you get the green light from the medical department, you need to introduce yourself slowly and just assess how the knee reacts.
"It was a severe injury and now we need to make sure that slowly he plays in 11-a-side games, because I think that he is going to be an important player for us in the second half of the season."
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