The BBC claims that Nantes have threatened the Welsh club with legal action if the payment is not made within the next 10 days.
Reports of Nantes' demands come amid the discovery of a body aboard the wreckage of the plane.
According to Sky Sports News, Cardiff have not yet paid any of the £15m fee agreed for the Argentine striker.
The light aircraft was later discovered lying in the bottom of the English channel after days of endless search for the missing player and pilot.
Authorities haven't said if the body located by an underwater camera was Sala or pilot David Ibbotson, the only people on board.
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The Telegraph reported a legal letter from Nantes was emailed to Cardiff on Wednesday (NZ time) to request urgent payment, which was the second demand in the space of a week.
Sala was making the trip to Cardiff after the transfer to the Premier League club.
Cardiff are reported to be committed to honouring the deal but not until they have been provided with sufficient documentation.
The Piper Malibu N264DB which was carrying Sala and Ibbotson has recently been found with one body among the wreckage, but it has yet to be identified.
The Air Accidents Investigation Branch (AAIB) are now trying to recover a body from the wreckage, although there is no confirmation whether the body identified is Sala's.
Bordeaux, Sala's previous team, are thought to be due 50% of the transfer fee as per the terms of the deal which had taken him to Nantes.