The England left-back has been ruled out for up to six weeks with a broken bone in his right foot but the Toffees boss said the focus in that period will be on the defender's fitness and not his future.
Manchester United failed with a bid for the 28-year-old in the summer and former Everton manager David Moyes could return with a new offer when the January transfer window opens.
Baines has just over 18 months remaining on his current deal but Martinez said they were in no rush to tie him down in the long term.
"I think the injury doesn't change anything," said Martinez.
"All our plans have always been the same. We want to have Leighton for the long term and that will never change.
"The injury is a setback as you can imagine but we will use it to regenerate him, to give him a bit of a breather as he has been playing week in, week out and has had a lot of big demands on him because he's been playing international football also.
"It is a period we are going to use in our favour but, in terms of his contractual situation, it will never change what our thoughts were and our strategy behind the scenes."
There has been talk of a new deal for full-back Tony Hibbert, who has made just one 66-minute Capital One Cup appearance this season because of a calf injury.
However, Martinez said while he wanted to keep the 32-year-old defender, whose contract expires next summer, there had been no developments.
"Tony Hibbert and (fellow academy graduate) Leon Osman are unique characters. They are more than players, they represent the club and give direction to the new players coming in, youngsters and foreigners," said the Spaniard.
"Tony is someone I want to have at the club as long as we can.
"Another aspect is to see how he is after the injury. All he wants is to focus on his fitness and fight to earn a place in the team.
"I didn't think it is the moment to look any further. He is a gem of a person, a special person to have at a football club."
Martinez received a lift on the injury front this week with centre-back Antolin Alcaraz, who has yet to make his debut following a summer move from Wigan because of injury, improving his match fitness.
"Alcaraz is ready now. We had a behind-closed-doors friendly earlier in the week and he came through that," said the Toffees boss.
"Now it is just measuring his match fitness and being able to give him the time he needs to pick up the pace.
"He is fully fit, anxious to come back and help the team which is a positive point.
"It is important he is fully fit for the Christmas period because we are going to need everyone and Antolin needs to be ready.
"What I'm not going to do is push him too early after the spell he had to endure on the sidelines."