Earlier on Wednesday reports emerged that the Ligue 1 club were demanding six of the €15 million (£13m/$17m) from the Premier League club for the Argentine forward.
The plane carrying Sala – and pilot David Ibbotson - from Nantes to Cardiff went missing on January 21 , with Guernsey Police undertaking a search for the Piper Malibu aircraft in the following days.
After that exploration was stopped, a privately-funded search for the aircraft was launched and the plane was found on Sunday, with the Air Accidents Investigation Branch (AAIB) confirming one passenger is visible in the submerged wreckage.
The AAIB have now recovered the body and, out of respect for Sala's family, Dalman says Cardiff will allow an ongoing process to be completed before dealing with the payment to Nantes.
"The only thing I can say, because it is a sensitive subject, is that I confirm that what you are saying [that Cardiff haven't paid the first instalment] is true," he told L'Equipe .
"And to be honest, I do not want to say anything more at this time."
When asked why they are yet to pay, Dalman added: "The first reason is that the body has not been recovered yet.
"We must show respect to the family. There is a process for recovering the plane. It's too early for us to comment.
"[We will pay] when we think it's the right time to do it.
"I don't think Cardiff said we were not going to pay."
The AAIB said in a statement released on Wednesday: "In challenging conditions, the AAIB and its specialist contractors successfully recovered the body previously seen amidst the wreckage. The operation was carried out in as dignified a way as possible and the families were kept informed of progress.
"Unfortunately, attempts to recover the aircraft wreckage were unsuccessful before poor weather conditions forced us to return the ROV to the ship. The weather forecast is poor for the foreseeable future and so the difficult decision was taken to bring the overall operation to a close. The body is currently being taken to Portland to be passed into the care of the Dorset Coroner.
"Although it was not possible to recover the aircraft, the extensive video record captured by the ROV is expected to provide valuable evidence for our safety investigation."