Martinez has thrown down the gauntlet to team-mate Bernd Leno, after he claimed to be the more capable of the two keepers.
Speaking to the Arsenal En America podcast this week, Martinez said: "He (Leno) has more professional matches than me, but in qualities I am equal to or better than him.
"My goal is to reach the Argentine national team, I have the qualities.
"I need only a little more playing time. I want to add minutes, make a great season, be Arsenal's number one and have chances of being in the team that plays the Copa América 2020."