The Argentinian 27-year-old got his chance to stake a claim when regular No. 1 Bernd Leno was injured in June.
Martinez then played the final eight Premier League games of the season and saw out the FA Cup run, keeping a clean sheet in the semis against Manchester City and helping win the final itself, 2-1 against Chelsea.
Now he has no intention of relinquishing his place between the sticks and says he’ll only remain if he stays first choice, as he has designs on being the starter at international level, too.
“I have shown the club that I can play for them and when I return next season I need to have more games,” he told Argentine outlet Continental.
“That is the only way I will stay at Arsenal.
“My target is to consolidate my place with Arsenal and to reach the Argentinian national team as number one.
“I won’t stop until I get that and if I don’t play for Arsenal, then clearly I would move on.”
Martinez may now be in line to earn a new contract at the Emirates, where he has two years left on his current deal, though it appears he’ll only put pen to paper if given assurances about his role in the team.
Leno, meanwhile, is still recovering from his knee injury and has three years left on his own contract.