Barcelona star Lionel Messi was handed the four-game ban after verbally abusing a match official in Argentina’s win over Chile in March.
The 29-year-old was also handed an £8,000 ($10,000) fine for his outburst.
He has already missed the 2-0 defeat to Bolivia and could be excluded from World Cup qualifiers against Uruguay, Paraguay and Venezuela.
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But Argentine newspaper La Nation claim the playmaker could be set for a reprieve.
Earlier this week Chiqui Tapia, the president of the Argentine FA, confirmed he will head to Switzerland for the meeting.
According to the report, Messi will be summoned to a FIFA hearing in Zurich on 4 May.
Barcelona star Lionel Messi has been banned for four international games
Messi was banned for his comments aimed towards officials
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Messi scored twice for Barcelona yesterday
The Argentina captain will be asked to explain his actions and his presence will boost his chances of getting the ban reduced.
Argentina have endured a miserable World Cup qualifying campaign and currently sit outside the South American spots for Russia 2018.
Meanwhile, Messi scored twice in Barcelona’s 3-2 win over Real Sociedad yesterday that keeps them three points off Real Madrid, who required a last-minute goal from Isco to beat Sporting Dijon 3-2 yesterday.