Both parties have said they were "disappointed" by the outcome of a Fair Work Commission conciliation.
Rugby Australia terminated his contract in May after the evangelical Christian said "Hell awaits" gay people.
"Thanks to those who have supported me. I will continue to stand up for the freedom of Australians," said Folau.
His lawyer George Haros said that "unless things change we'll be heading to court".
The 30-year-old, who also had his contract terminated by New South Wales Waratahs, believes the dismissal is an unlawful act of religious discrimination and could now apply to have his case heard in Australia's Federal Court.
Rugby Australia and the NSW Rugby Union issued a joint statement, which said: "Rugby Australia and NSW Rugby Union are incredibly disappointed that the Fair Work conciliation has been unsuccessful and did not reach a resolution.
"We remain confident in our processes and will continue to do what is required to defend the values that underpin our game."
After the first GoFundMe page set up to help the former player cover the costs of Folau's legal action was shut down, a second raised more than two million Australian dollars (£1.1m) in just two days.