Jara was at the centre of the controversy that saw Uruguay's Edinson Cavani sent off on Wednesday in the second half of a match which Chile went on to win 1-0.
Having already been booked, Cavani picked up a second yellow card for raising his hand to Jara's face, with the latter falling to ground theatrically.
Replays then revealed the provocation that the striker had received, with Jara appearing to prod the Paris Saint-Germain star in the backside with a finger.
Mainz sporting director Christian Heidel has now indicated the Bundesliga club are less than impressed with their player's conduct and are happy to sell the defender.
"He knows that if an offer comes, he can go," said Heidel to Bild.
"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."
It is unclear as of yet whether Jara - contracted to Mainz for another season - will receive a suspension, with Chile set to face Peru in the Copa semi-finals on Monday.