Representatives from both parties met at the Fair Work Commission in Sydney on Friday for a mediation hearing - the first formal step in the unfair dismissal case.
"We are disappointed that we were unable to reach settlement with Rugby Australia today," Folau's lawyer George Haros told reporters.
"It appears as though that unless things change, we'll be heading to court."
Folau said he was "very, very disappointed by the outcome".
"But I'd like to thank all those that have supported me throughout this time. I will continue to stand up for the freedoms of all Australians," he said.
Folau had been hoping RA would apologise for terminating his multi-million dollar contract over a social media post in April condemned as homophobic.
The 30-year-old's post paraphrased a Bible passage saying "drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolaters" would go to hell unless they repented.
The committed Christian argues he was unfairly dismissed on religious grounds.
Folau is seeking $10 million in damages from RA and wants his contract reinstated.
In a video posted on his website before Friday's meeting, Folau said he hoped RA would accept his termination was unlawful and reach an agreement about how to fix the "mistake".
"First and foremost, I am hoping for an apology from Rugby Australia and an acknowledgement that even if they disagree with my views, that I should be free to peacefully express my religious beliefs without fear of retribution or exclusion," he said.
Folau claimed on Thursday that RA had offered him money to remove the post at the centre of the dispute, and he had declined because sharing the Bible was one of his duties as a Christian.
"I couldn't do that ... I couldn't live with that," Folau said.
"It certainly comes from a place of love and it's nothing personal."
But RA says Folau's claim is "completely untrue" and it never offered him money to remove the posts.
More than 20,000 people have donated about $2.2 million to help fund Folau's legal battle via a campaign page set up by the Australian Christian Lobby.
The ACL effort replaced an earlier campaign on GoFundMe, which was taken down by the platform for breaching its service guidelines.
"I want to thank you all for your prayers and your support. You have made it possible for me to stand up for every Australian of faith," Folau said.
"I know we are strong enough to tolerate different views without firing people from their jobs for expressing religious beliefs that not everybody agrees with."
