The Professional Tennis Players' Association (PTPA) filed a class-action lawsuit in March saying the ATP, WTA, International Tennis Federation and International Tennis Integrity Agency had indulged in anti-competitive practices and showed disregard for player welfare.
Organisers of the four Grand Slam events, including the Australian Open, were added to the case in September.
The men's ATP Tour has previously said it believed the case was without merit while the women's WTA Tour defended its record of growing women's tennis and said the lawsuit was "baseless".
On Wednesday, lawyers for the PTPA, co-founded in 2020 by Djokovic and Vasek Pospisil, filed a letter to the US Southern District Court in New York saying there had been fruitful talks with the organisers of the Australian Open.
"Plaintiffs and Tennis Australia are engaged in substantive and productive bilateral settlement discussions and believe that a settlement as to plaintiffs' claims against Tennis Australia is likely in the near future," the PTPA's lawyers wrote.
Both parties want to halt proceedings while they reach a deal, with the stay to apply only to Tennis Australia, not the other defendants.
Tennis Australia confirmed the development.
"If the New York court approves a settlement between the parties, Tennis Australia will exit the litigation," it said.
Neither party gave any details of what a potential deal may entail.
In its lawsuit, the PTPA accuses the various governing bodies of paying "artificially low compensation to professional tennis players" and imposing a "draconian" ranking system that forces them to compete in certain tournaments.
It also calls the gruelling 11-month schedule unsustainable, says players are made to compete in extreme heat and during the early hours of the morning and that different tennis balls used in different events are causing chronic injuries.
While the world's elite tennis players can earn fortunes, those further down the rankings often struggle to balance a meagre income with the costs of coaching, travel and accommodation.
Players are expected to compete in a set number of mandatory tournaments every year or risk penalties that include the loss of ranking points.
Tennis Australia is currently preparing for the Australian Open, which begins in Melbourne on January 18 and kicks off the new Grand Slam season.
