Everton boss Martinez makes clear he wants Barry stay
Barry's loan deal from Manchester City finishes at the end of this season and Martinez is keen to keep him.
He said: "I would love to work with Gareth for longer than that. He is enjoying his football. He takes it game by game and he will make a decision on what he wants to do next.
"Going to the World Cup or not may have a bearing on that decision, but I am just happy to see Gareth enjoying his football and having such a big, big season for us."
Barry said of his club future: "It will just be a conversation to have at the end of the season.
"The manager said that when I signed there would be no pressure on myself or the club to make decisions around this time.
"I'm enjoying working with the manager, this is a great bunch of lads and it is a fantastic club. So certainly from that angle it is perfect."