The Iranians' campaign in the Australian-hosted tournament started last weekend just as the US and Israel launched air strikes on Iran, killing the Islamic Republic's Supreme Leader Ali Khamenei.
The team was eliminated on Sunday after losing 2-0 to the Philippines. Fans waved the pre-1979 Iranian flag, booed the national anthem and tried to prevent the team coach from leaving afterwards, chanting "Save our girls!" amid concerns for their safety after their anthem silence.
More than 66,000 people have also signed a petition calling on the Australian government to ensure the players, who are on the Gold Coast in Queensland, do not leave "while credible fears for their safety remain".
Beau Busch, FIFPRO president for Asia and Oceania, said the union had been unable to contact the players to discuss whether they would like to seek asylum in Australia.
"The reality at the moment is that we're unable to get in touch with the players. That's incredibly concerning. That's not a new thing. That's really been since the repression really dialled up in February, January," Busch told reporters.
"So we're really concerned about the players, but our responsibility right now is to do everything within our power to try and make sure that they're safe."
Busch said the organisation was working with FIFA, the Asian Football Confederation and the Australian government to ensure that "every bit of pressure is applied" to protect the players and give them "agency around what happens next".
"It's a really challenging situation," he said.
"There may be players that want to return. There may be some players within the group that would like to seek asylum and would like to stay in Australia for longer."
'Pinnacle of dishonour'
The players' decision to stand in silence during Iran's anthem before their first match against South Korea was labelled by a commentator on Islamic Republic of Iran Broadcasting as the "pinnacle of dishonour".
"Traitors during wartime must be dealt with more severely," presenter Mohammad Reza Shahbazi said.
When they sang the anthem and saluted before their second match against Australia, it sparked fears among human rights campaigners the team had been coerced by government minders.
Iran coach Marziyeh Jafari has said they were keen to return home. "We are very impatiently waiting to return," she said during a post-match press conference.
Most of the airspace in the Middle East remains closed as a result of the war.
When asked about whether Australia would grant the players asylum, Matt Thistlethwaite, the assistant minister for foreign affairs and trade, said the government could not "go into individual circumstances for privacy reasons".
"Anyone that seeks to come to Australia or applies for a visa obviously must meet the conditions, but I can't go into the specifics of details," he told Sky News.