The Barcelona star missed Saturday's 2-0 win over El Salvador in Washington due to swelling on his right foot, and it remains unclear whether he will have recovered in time for this clash.
"The third training day he was unable to wear the right boot," head coach Gerardo Martino said.
"We all understand that the fans had hoped to see him play, but he was really unable.
"Leo always tries to play. We'll wait for his recovery until the last minute before the kick-off, but we won't risk him.
"If he remains this way, he won't play on Tuesday."
A Nestor Renderos own goal and a late Federico Mancuello effort on his debut earned Argentina a win against El Salvador, who were less than impressed when the Kazakhstan national anthem was played before kick-off instead of their own.
That was the in-form Mancuello's fourth goal in as many matches after scoring in three successive games for Independiente in the build-up to his international bow.
Ecuador, meanwhile, went down 1-0 to Javier Hernandez's winner for Mexico in Los Angeles, as they were left to rue Miller Bolanos' missed penalty 17 minutes from time.
That match marked Gustavo Quinteros' first game in charge after he took over from interim boss Sixto Vizuete in January, and the new coach was encouraged by the display against Mexico as he begins to look forward to the Copa America in June and the World Cup qualifiers beyond that.
"We'll try to get to the Copa America in much better form, but we mainly focus on the World Cup qualifiers," he told Ole.
"We have to organise ourselves defensively. We can correct this by working hard. In the Copa America we'll play matches similar to these two.
"We are looking for a different direction and we need a long time training, several matches, a long time altogether.
"I liked the way we played against Mexico, as in several moments of the game the team played as I want - pushing forward and having good possession."
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