The 32-year-old's impressive form at Goodison Park, having been deemed surplus to requirements at Manchester City, has started to attract interest from other clubs with Arsenal the latest to be linked.
But while Martinez believes Barry is playing well enough for an England recall, he is confident there is no need to bring forward planned talks on the player's future ahead of a summer when he will become a free agent.
"It (speculation with other clubs) doesn't change anything. I trust him implicitly," said the Toffees boss.
"He has incredible human values. He's a person who needs to make footballing decisions.
"He's enjoyed an incredible career and is in a position that he can choose where his football happiness is going to be.
"From the beginning Gareth was a massive target of ours: he was available in the summer for other clubs and he decided to come to Everton.
"We did everything to bring him to the club and the relationship was to make sure he could go back to his very best, enjoy his football and have a big role at Everton.
"We were very clear with what we wanted from Gareth - to put him in an environment where he could be important, we could use his experience and he could enjoy his football. That was always the case for this season.
"Our agreement was in the summer we would sit down and it would be a question of what is best for Gareth.
"At the end of the season we will sit down and see if we've reached every single target we had and I'm sure Gareth is only focused on the games ahead and winning as many as we can for Everton.
"Nothing else matters. When you get interest from other parties and clubs looking at our players it is a good sign because the players are doing well and that is compliment I take with happiness."
Martinez could not be more happy with how Barry's loan deal has worked out as he has become an integral part of the manager's plans in how he wants his side to play.
He believes Barry has regained the form which should put him back in England contention, although there seems to have been no inclination from Roy Hodgson to even consider a recall.
"You saw the way he performed at the weekend (in the 1-0 defeat at Tottenham)," said the manager.
"It's a joy to have him at the club and his only focus now is to play as well as he can in every single game and I'm sure that the England squad could benefit from that level of performance.
"I enjoy working with him. He works exactly how we set out to do in the summer and I still think he's the best English player in that position.
"I'm just glad he's been able to show that at Everton, which could have a massive effect on him internationally."
Defeat at White Hart Lane was only Everton's fourth in the league and on the three other occasions they have bounced back with a victory and Martinez expects a similar response at home to Crystal Palace on Wednesday.
"There is a real unity in the dressing room which is wrapped up with incredible character and great tenacity," he said.
"There is a difference between performing badly and needing another game to perform well - this is not the case as we performed really well at the weekend and we didn't get what we deserved.
"It is another test for us to react. The character and the personality of this dressing room has never been in doubt, it is one of the biggest strengths we have."
Martinez plans to give on-loan Monaco striker Lacina Traore, who arrived last month with a hamstring injury, his debut from the bench.
"Lacina is progressing really well and I didn't expect him to be available just yet but it is just giving him match-fitness," he added.
"I think he will be involved somehow but he is not ready for 90 minutes.
"He will have a massive role to play in our final games so it is giving him the opportunity to be on the pitch at the right time."