The left-back has been sidelined since limping out of last month's Merseyside derby clash with Liverpool due to an ankle injury, but is approaching full fitness once again
Martinez revealed on Friday that Baines, who has not featured since being taken off in the 3-3 draw with Liverpool last month, is close to being available for selection again.
Baines has an outside chance of being in contention for Everton's Premier League clash with Swansea City on Sunday, although Martinez is keen not to rush the England international back too soon, hinting that he may wait until next weekend's game with Southampton to call upon the 29-year-old.
|6/4||Everton are 6/4 with bet365 to beat Swansea City|
"[He is] not far away, he trained at the beginning of the week. We'll assess him and I expect Leighton to be available, if not this weekend, the week after," Martinez said on Friday.
"He is not too far away, which is a beautiful Christmas present as you can imagine.
"It depends on the next two days but we need to make sure we're not rushing him back."
Martinez also reaffirmed his commitment to strengthening his squad in the January transfer window due to long-term injuries to the likes of Darron Gibson and Arouna Kone.
"I'm going to be judging how the squad is and I've got two long-term injuries who were going to have a big role," he said.
"I've got two long-term injuries with Gibson and Kone. I would like to replace them for the short term and I will look into that.
"I'm delighted with the squad and the blend we have. Bringing in players for the sake of it can damage what you have."
Martinez stated that no bids have been received for Nikica Jelavic or Johnny Heitinga, with the pair having fallen out of favour during the Spaniard's time at Goodison Park.