Television images showed the 29-year-old defender, who has a contract until 2016, prodding Uruguayan striker Edinson Cavani during Chile's 1-0 victory in Santiago on Wednesday.
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.
(Reporting by Karolos Grohmann; Editing by Peter Rutherford)
Share
