The Toffees know that the experienced midfielder will spend the remainder of the current campaign on their books after agreeing a season-long switch from Manchester City.
With there seemingly no future for Barry at the Etihad Stadium, as he has entered the final year of his contract, he will require a new club in 2014.
Everton have seen enough from the England international to suggest that prolonging his stay would be beneficial to all concerned, but intend to leave it until next summer before putting terms to the 32-year-old.
Pressed on whether a deal could be done in January, Martinez said in the Daily Star: "No, Barry is here until the end of the season, that cannot be affected.
"All we want is for him to enjoy his football and to be effective for Everton and then we will take it from there.
"We are blessed with quality in the squad. We don't want to lose any player, but there is a chance now for others in the squad. Then we will assess in January."
Martinez added on Barry, who could yet force his way into England's squad for the 2014 World Cup: "When you get to work with someone who has played more than 500 Premier League games, you know that they don't need any extra motivation to be at their best.
"I don't think it makes any difference if he sees he has an opportunity to play for England again or not.
"But I see the standards he brings on a daily basis and see Gareth as a very, very valuable option for England.
"Only time will tell, but what he brings onto the pitch is very difficult to find. You don't get many options where you have someone of that experience, know-how and tactical awareness."