The Islamic Republic of Iran Wrestling Federation (IRIWF) has proposed that three-nation tournaments are held every year under a banner of "World Solidarity for Wrestling".
A letter outlining the proposal has been sent to United World Wrestling (UWW) President Nenad Lalovic, according to Press TV.
The idea is for "symbolic" contests to be held in freestyle, Greco-Roman and women's disciplines, bringing together countries that have historically experienced political tensions.
Iran, the United States and Russia would compete in the freestyle competition, with Russia and Turkey joining the Iranians in the Greco-Roman event.
The women's tournament would feature Russia, the US and Japan.
Milad Tower in Iran's capital Tehran has been suggested as a possible venue, as has Red Square in Russian capital Moscow.
Times Square in New York City could also play host, the IRIWF said.
According to the Iranian governing body, the events could also help promote wrestling globally which could in turn lead to its Olympic place being maintained.
Wrestling was removed from the Games programme for Tokyo 2020 in February 2013, but campaigned to be re-added and was reinstated in September of the same year.