Baines has been out of action since fracturing a toe in the Merseyside derby with Liverpool on November 23.
Sunday's match at Swansea comes too soon for Baines, but Martinez is not yet ruling him out of the Boxing Day match with Sunderland.
"He is not far away," Martinez said.
"He trained at the beginning of the week and we are going to assess how he responds to it.
"I expect Leighton to be available probably, if it is not this weekend, then the week after.
"It is just measuring well that we don't rush him back too early. But I would say he is not too far away, which is a beautiful Christmas present as you can imagine.
"If he has no reaction, he will be available to play on the Boxing Day, or possibly even earlier. But it just depends on how the next two days show up in his foot."
Darron Gibson and forward Arouna Kone remain on the long-term injured list, and Martinez expects to dip into the transfer window in January - though he would not be drawn on whether Manchester United's Wilfried Zaha is a target.
Martinez also said he had not had any approaches for striker Nikica Jelavic or defender Johnny Heitinga.
The pair have been left out for most of the season, but Martinez said: "They are two players with incredible experience and they have been very important day-to-day.
"I can understand their frustration and down to the respect for what they have done I will always be helpful and try to understand their position.
"They are full internationals and looking to get to the World Cup, so you understand they have to play minutes, but in many ways I would love for them to stay here and play their role as they have been doing until now."