The original hearing at the Nantes court was set for September 22nd, but that has now been rescheduled for December 8th after the Welsh club provided further evidence, leading to the French side requesting a delay.
Sala, a 28-year-old Argentine striker, died when the light aircraft taking him to the Welsh capital came down in the English Channel on January 21st, 2019, two days after he had signed for the then-Premier League side.
"A late communication, in the middle of August, of new conclusions and documents from Cardiff have legitimately led Nantes to argue that the case is not ready to be heard on September 22nd," the Nantes source told AFP.
Cardiff released a statement criticising Nantes's position and said that the Ligue 1 side needed to take responsibility for their actions.
"This stance is all the more surprising given the confidence shown by FC Nantes until now, which claimed that the case had already been decided in its favour and described the CCFC's argument as 'absurd'," they said.
"Six years after the tragedy that claimed the life of Emiliano Sala, FC Nantes must be held accountable - both for the world of football and for the player's loved ones," they added.
The two parties have wrangled for years over Sala's transfer fee as his death happened before he ever played a match for Cardiff but after the two clubs had agreed to his switch.
FIFA ruled in Nantes's favour and ordered Cardiff to pay the French side just over 11 million euros (at the time £9.45m), corresponding to the last two instalments of the 17 million euro (£15m) fee agreed between the two clubs.
The Bluebirds, who were relegated from the Premier League in 2020, counter-sued two years ago, arguing that Nantes, through their agent Willie McKay, had arranged the flight and thus they should take responsibility for the monetary losses.
Cardiff say the crash, which deprived them of an important new signing, and their subsequent relegation, cost them 120 million euros (£104m).