Sala, 28, was Cardiff’s record signing, announced in January.
The Argentine striker died in a plane crash while travelling from France to join his new club.
Fifa sent a letter to both clubs stating that should they miss the deadline, they will issue its own ruling, which is subject to appeal.
“We can confirm that a letter was sent to the parties on behalf of the chairman of the players’ status committee,” Fifa said.
“Please understand we cannot comment further at this stage.”
Sources at Cardiff confirmed receipt of the letter from Fifa.
Fifa president Gianni Infantino has previously said he hoped the two clubs would be able to reach an agreement themselves.
Cardiff have refused to make interim payments, claiming the deal was not legally binding.
The Bluebirds told world football’s governing body that Nantes’ conditions for completion of the deal were not fulfilled and Sala was not registered as a Premier League player.
Nantes claim the required paperwork was completed.
Sala and pilot David Ibbotson, 59, crashed in the English Channel on 21 January.
The footballer’s body was recovered from the wreckage of a crashed plane but Mr Ibbotson, from Crowle, North Lincolnshire, has still not been found.
Sala was exposed to high levels of carbon monoxide prior to the fatal crash, a report has revealed.