Everton have a £1million deal in place with parent club Manchester City for Barry, but Martinez admitted the player’s decision would be governed by where his “next footballing chapter” should take place.
“We will talk after the Hull game,” said Martinez, who is keen on Manchester United midfielder Tom Cleverley. “We will sit down and I’m sure we will get a straight answer in one way or another.
“It’s not about finding a good contract or financial package, it’s more about the next footballing chapter and where he can enjoy it.
“He has loved his time at Everton but you don’t know where his next step is. Does he want to go abroad? Experiment with a different culture?
“It’s important that we try to keep him at the club but, in the same way, if he doesn’t stay, it’s our job to make sure the next squad in the next window is as strong or stronger than what we have.”
Barry, 33, has no pressure to make a decision straight away and could wait until later in the summer to see what offers roll