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."