Jara was the subject of widespread revulsion on social media after photos and camera footage clearly showed him jabbing a finger into the back of Uruguay striker Edinson Cavani's shorts during Wednesday's quarter-final, won 1-0 by Chile.
The lurid provocation ultimately led to Cavani being sent off after the Paris St-Germain star flicked a retaliatory hand into Jara's face.
Mainz boss Christian Heidel said the Bundesliga club was ready to sell the 29-year-old player.
"He knows it -- if we receive an offer, he can leave," Heidel told Bild newspaper.
Jara joined Mainz from English side Nottingham Forest last year but featured in just 17 games during the season.