The two clubs have been in dispute since the 28-year-old striker died in a plane crash in the English Channel on January 21, two days after Cardiff had announced him as their record signing "subject to international clearance".
FIFA had originally ordered evidence to be submitted by Wednesday to adjudicate in the dispute.
But world football's governing body has now granted an extension until April 15.
"Cardiff City has requested and been granted an extension to the deadline to respond to FIFA on this matter," said a club statement.
"Cardiff City recently wrote to FC Nantes proposing a meeting to discuss issues surrounding the Emiliano Sala tragedy and planned transfer, in line with Fifa's request for our two clubs to come to a resolution directly.
"To date, Cardiff City has not received a response from FC Nantes."
The Ligue 1 club lodged a complaint with FIFA over Cardiff's refusal to pay the first £5m instalment of the Sala transfer fee.
But FIFA president Gianni Infantino made it clear more than a month ago that they would prefer Cardiff and Nantes to resolve the dispute among themselves.
It is understood Sala's Cardiff contract was rejected by the Premier League because it contravened signing-on fee rules.
Sala died before a revised one could be signed and there is a dispute about whether he had agreed to do so before his death.
Press Association Sport reported last month that Cardiff also planned to tell FIFA that the non-fulfilment of legally-binding clauses in the transfer agreement they struck with Nantes for the player made the deal invalid.
Without these clauses being fulfilled, Cardiff say Sala was perfectly entitled to join another club with more than a week of the January transfer window remaining.
Cardiff had nothing to do with the plane on which Sala and pilot David Ibbotson were killed, saying the player had been offered a commercial flight to travel from France to Wales.
Weekend reports also suggested that Ibbotson was not qualified to fly at night, as he is thought to have been colour blind and his licence restricted him to flying only in daytime hours.