German club Mainz 05 are ready to offload Gonzalo Jara after the Chile international whipped up a storm at the Copa America by sticking his finger up the backside of an opponent before falling to the floor theatrically when the player retaliated.
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Cavani reacted by pushing Jara away with the back of his hand but the Chilean fell to the ground as if he had been punched.
The Brazilian referee showed Cavani his second yellow card of the game and sent him off.
"He knows that if an offer comes he can go," Mainz sports director Christian Heidel told Germany's Bild newspaper on Friday.
"We do not tolerate that. More than the prod, however, it is what comes afterwards that makes me angry. I hate theatrics more than anything."
Images of the incident were all over social media and it was the main talking point from the match, which sent Chile into the last four of the competition for the first time in 16 years.
Jara received severe backlash on social media for his theatrics.
Jara's fate remained uncertain on Thursday, with South American football's governing body CONMEBOL saying they would only lodge a disciplinary case against the Chilean if they received a formal complaint.
Uruguay coach Oscar Tabarez could not hide his anger at the incident.
"You can see what happened and what the challenge was. I refer you to the television and photos of it, it is all there," said Tabarez.
"I can see that the referee has not seen it, but the linesman had to be able to see it from his position."
But the football world was unanimous in their disgust of the incident, with many expressing sympathy for Cavani, whose father was arrested earlier this week for his part in a fatal traffic accident.
"Particularly when you consider it was Cavani, and all the other problems he's had this week, it was shameful," Argentina coach Gerardo Martino said.
"There is absolutely no justification for it whatsoever. And on top of all that, Cavani barely touched him," Martino added.
Colombia coach Jose Pekerman also decried Jara's actions, saying the move had tarnished the image of the sport in front of a global audience.
"We all want to win and there is pressure on everyone to win, but the contest has to be noble," the veteran Argentine-born coach said.
"Football is a sport that the whole world watches. There are certain rules that must be respected."
Image: A video grab of Chilean Jara prodding Colombia's Edison Cavani during their Copa America match on Wednesday
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