The Bluebirds are refusing to make interim payments for the striker , who died in a plane crash on 21 January.
Cardiff will tell world football’s governing body Fifa 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.
The French club referred the matter to Fifa, who want Cardiff to submit their evidence by 3 April.
Sala, 28, was Cardiff’s record signing, announced on Saturday, 19 January.
The Argentine died when an aircraft piloted by David Ibbotson, who is still missing, crashed into the English Channel near Guernsey.
The club was due to pay a first instalment on 20 February.
A Cardiff source said the transfer agreement stipulated – at the request of Nantes – that the Football Association of Wales and France’s Ligue de Football Professional had to confirm the registration to both clubs by 22 January, along with confirmation of the international transfer certificate being released.
The Premier League also had to clear the registration.
The Bluebirds insist the terms of the contract maintains that if any parts of that arrangement were not confirmed, then the deal would be null and void.
- Ligue de Football Professionel had not contacted Cardiff either before or after 22 January.
- The FAW did not confirm with Nantes.
- The Ligue de Football Professional did not confirm with Nantes until 25 January.
It is thought the notifications clause was inserted because if the deal fell through, both Cardiff and Nantes would have had time to seek a new player before the January transfer window closed on 31 January.
BBC Sport has also learned arrangements for a signing-on fee did not meet Premier League rules and so had been rejected by the league.
A Cardiff spokesman would not comment on specific details but said: ”The club is aware of Fifa’s request for a response by 3 April and is processing that accordingly. We have no further comment at this stage.”
Nantes say they completed all the necessary paperwork and have pointed out Fifa registered the international transfer certificate on 21 January.
They say they have been fully compliant with Fifa’s rules.