The body was seen in the Piper Malibu N264DB on Monday, two weeks after the plane vanished near Guernsey.
Investigators have not been able to recover the aircraft which was flying from Nantes to Cardiff after Sala transferred from the French city's team to the Welsh capital's Premier League club.
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.
A body was spotted in underwater images of the wreckage and Britain's Air Accidents Investigation Branch (AAIB) has launched an operation to try and recover it.
"The operation was carried out in as dignified a way as possible and the families were kept informed of progress".
The AAIB also confirmed attempts to recover the wreckage were abandoned due to bad weather conditions, and their recovery mission was now over.
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A decision has yet to be taken on whether to raise the wreckage to the surface.
"We expect our next update to be an interim report, which we intend to publish within one month of the accident occurring".
Regional newspaper Ouest-France quoted an anonymous source at Nantes calling Cardiff's attitude "hypocritical", accusing them of "wanting to buy time".
The AAIB warned the weather is expected to be poor in the coming days, and so the overall operation is being ended.
Sala was signed by Premier League side Cardiff City in January for a club record fee of £15million, before the Argentine striker and his pilot went missing.