Baines, who is pushing Ashley Cole as England's number one left back, suffered a fractured toe in the 3-3 draw with Liverpool last month, since when Costa Rica's Bryan Oviedo has seamlessly slotted into Everton's back four.
Martinez confirmed that Baines was close to a return on Friday, perfect timing as the high-flying Toffees prepare for Premier League matches at Swansea City on Saturday followed by home games against Sunderland and Southampton.
"The prospect of having Bryan and Leighton fully fit is a great challenge and I am very satisfied with it. I wouldn't like to be in a position where I didn't have that dilemma," Martinez told a news conference.
"Leighton has already been introduced to training. We now need to see how the injury reacts. If there is no reaction, he will be available to play on Boxing Day, possibly even earlier.
"It just depends on how the next two days show in his foot. He's not too far away but we need to make sure we don't rush him back too early.
"The headache at left-back is the sort of headache that you want. You would love to have that problem everywhere across the park. We have that in other areas and we have been using it really well when players are hitting good moments of form."
Everton have lost only one league game this season and are four points behind leaders Arsenal as they prepare for three winnable-looking Christmas fixtures.
"It's a remarkable achievement, only one defeat in 16 games," said Martinez before his return to his old club Swansea.
"This is a huge period for the club. We know this period is going to be vital with so many points at stake."