Mainz 05 have told under-fire Chile defender Gonzalo Jara that he can leave the club following his conduct in a recent Copa America quarter-final with Uruguay.
Cavani lashed out but appeared to make minimal contact with the 29-year-old, who went to ground clutching his face, and Mainz sporting director Christian Heidel says that he will listen to offers.
"He knows that if an offer comes, he can go," Heidel told 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."
Uruguay defender Diego Godin has urged Conmebol to issue a Luis Suarez-type punishment, after Suarez was suspended for four months and given a nine-game competitive international ban for biting Giorgio Chiellini last year.