According to the source, the first instalment of the 17-million-euro ($19.3 million) deal for the Argentine striker has yet to be paid, despite the transfer being finalised before the accident.
The body was seen in the Piper Malibu N264DB on Monday, two weeks after the plane vanished near Guernsey.
Sala and his pilot David Ibbotson have been missing since shortly after their plane took off from France on January 21.
BBC's report adds that Nantes are threatening legal action if they do not receive a payment from Cardiff within 10 days.
Cardiff have reportedly withheld payment until they are satisfied with the terms of the payment.
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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.
And Cardiff are "surprised" Nantes have made the demand while attempts are being made to recover a body from the plane wreck that was carrying Sala and pilot Ibbotson.
The Air Accidents Investigation Branch (AAIB) is considering the feasibility of lifting the wreckage from the seabed if it can recover the body.
It is understood that the agreement between the clubs was to process the payments in instalments over three years.
French club Bordeaux is also due a cut of the fee after Sala was under contract with them from 2012-15.
A recovery crew eventually found the aircraft in the ocean, with a body said to be visible in the wreckage.