Barry's contract with Manchester City expires in the summer and Blues boss Martinez says any talks of a permanent stay at Goodison Park will occur only at the end of the season - as per his agreement with the player.
Martinez said: "It doesn't change anything. I trust him implicitly.
"I enjoy working with him and I still think he's the best English player in that position and I'm just glad he's been able to show that at Everton, which could have a massive effect on him internationally.
"I'm glad there is talk because it means Gareth has been performing really well and there will be other options for him there. I still think the best for Everton and Gareth is to come.
"It's a hypothetical situation. All that matters is Gareth is fully fit, enjoying his football and being an important player at Everton Football Club. That's what we are enjoying at the moment. Everything else is not a concern at this time. He was sensational at the weekend."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball