Martinez has ruled out a January deal for Barry - because he trusts the midfielder to show Everton loyalty at the end of the season.
Martinez, whose side entertain Sunderland today, said: "We haven't changed our thoughts on the situation just because he has started really well.
"Gareth has been vitally important in what we have achieved so far this season and I would like that to be the case for many years to come. But we will talk about that in the summer.
"The agreement was for the season and for Gareth to just enjoy his football and I don't want to change that. I don't think there is a need."
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