The latest scrap has come between Angel Di Maria, a goalscorer in the final, and former France defender Adil Rami, who has been unhappy with Martinez's post-final antics and title celebrations.
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Post-final, Martinez made a vulgar gesture when he won the Golden Glove for the tournament's best goalkeeper, and at the celebration parade in Buenos Aires he held up a doll with Kylian Mbappe's face on it.
In the dressing room after the match, he was also seen asking for a minute's silence for Mbappe, which has been seen as disrespectful by many football figures.
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Rami has lost patience with Martinez and described the Aston Villa goalkeeper as 'the biggest s*** in football,' and Di Maria was not happy.
Rami then claimed Martinez was the 'most hated man' in football on Instagram, to which Di Maria responded: "El Dibu [Martinez] is the best goalkeeper in the world. Go cry elsewhere."
The ex-France defender then responded again, tweeting, "Can you teach me?", showing four pictures of Di Maria himself crying with the captions: 'When you lose', 'when you win', 'when you leave a club', 'when you see this tweet'.
Rami took advantage of Di Maria's history of getting emotional in big moments on the pitch and made it clear he wasn't having any of Martinez or the winger defending his teammate.
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Di Maria wasn't the only one to defend Martinez - his international teammate Leandro Paredes followed the same tune and previously asked Rami to 'say it without crying', poking fun of Les Bleus' final defeat.
There has been plenty of criticism directed Martinez's way - Crystal Palace manager Patrick Vieira wasn't happy with his antics, and neither was his own club manager, Unai Emery.
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Martinez is likely to return to action at the weekend for Aston Villa having missed his side's Boxing Day defeat to Liverpool.