Both parties are engaged in a court-ordered private mediation in Melbourne with a view to settling the dispute before a public trial in February.
Folau, who won 73 Australia caps, is claiming 14 million Australian Dollars for lost wages and sponsorships after his sacking in May.
The 30-year-old says he has lost out on the chance to play at two World Cups and the opportunity to become Australia captain.
Folau, a devout Christian, had his contract terminated by RA for a "high-level breach" after he posted "hell awaits... drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists and idolaters" on Instagram.
The former Waratahs back had been previously warned over his online posts in 2018.
RA is defending the suit, with chief executive Raelene Castle attending the negotiations.
"It's been a very long day," Folau's solicitor George Haros said after Monday's proceedings.
"Where we are at, is that we were unable to reach an amicable solution with Rugby Australia.
"However, where we stand is that mediation remains on foot. We are still hopeful of reaching an amicable agreement with Rugby Australia.
"We would like to thank the court mediators for the effort and look forward to reconvening in a few days to see if we can strike an agreement."
Discussions are expected to resume as early as Wednesday, with these negotiations coming after RA and Folau failed to reach a settlement in June and an unfair dismissal case began in court in August.
In a fresh controversy last month, Folau's comments linking the bushfires in Australia to gay marriage and abortion were slammed as "appallingly insensitive" by the nation's prime minister Scott Morrison.