The audio recording is said to be from a meeting at Mr Trump's New Jersey golf club in July 2021, which is around six months after he left office.
Two people familiar with the matter told CBS that Mr Trump can be heard acknowledging there are national security restrictions on a military memo because it details a potential attack on Iran.
He says it is still classified and should have been declassified before leaving the White House, one person said.
Mr Trump also says he wants to share information from the document but knows his ability to declassify it is limited because he is no longer president,
CNN reported.
It is not clear whether Mr Trump had the document during the meeting or was just describing it to several aides who were there. Other reports suggest the sound of rustling paper can be heard.
The tape appears to contradict Mr Trump's repeated argument that he declassified all material he removed from the White House. It could also prove to be a key piece of evidence if prosecutors seek to show the former president was aware he should not be in possession of classified documents.