Argentine-born coach Martino, who was Messi's coach at Barcelona during the 2013-14 campaign, was blunt in his assessment on knocking out his former player from the tournament.
"What would you do in my place? I know where I was born, I'll tell you the year, the name of the hospital, the city's area code," Martino told a prematch news conference on Friday. "But I have to do everything possible for Mexico to win."
While Mexico are heading into Saturday's match at Lusail Stadium with a point after a 0-0 draw with Poland, Argentina will be desperate to bounce back after a shocking 2-1 loss to Saudi Arabia in their World Cup opener.
Another loss for Argentina would mean a stunning early exit from the tournament for a team considered as one of the favourites to win the trophy.
It would also mean another edition of the World Cup failure for Messi, who has said that he is playing in his last tournament.
Martino was skeptical that he could do much to halt the efforts of the seven-time Ballon d'Or winner.
"Stopping him, it happens more often because he's having a bad afternoon than what we can do," Martino said. "The best footballer in the last 15 years, at least."
Before Mexico face Argentina on Saturday, fellow Group C members Poland and Saudi Arabia will take the field at Education City Stadium earlier in the day.
After the weekend games, Mexico will close out their group stage run against Saudi Arabia at Lusail Stadium on Wednesday, while Argentina will face Poland at Stadium 974, also Wednesday.