The prominent government critic was killed in Saudi Arabia's consulate in Istanbul last October.
The pro-government Sabah newspaper says the transcript is from a recording taken inside the consulate and later obtained by Turkish intelligence, the BBC reported on Wednesday.
It includes information such as the journalist's alleged last words.
Khashoggi wrote a column for the Washington Post newspaper and was based in the US before his disappearance. He was last seen entering the Saudi consulate in Istanbul on October 2, 2018 to obtain papers he needed to marry his Turkish fiancee.
His mysterious death piled scrutiny on Saudi Arabia, which released conflicting information regarding his disappearance in the aftermath.
Saudi authorities have since blamed a "rogue" operation for his murder and put 11 men on trial.
Sabah published two new reports this week on Khashoggi's death at the hands of a group they label a "hit squad".
Their latest report details information from the alleged recording. It includes details such as a forensic expert, part of a team sent from Saudi Arabia, allegedly referring to the journalist as an "animal to be sacrificed" prior to his arrival.
The Sabah report says Khashoggi, once inside the consulate, became suspicious and was told he had to return to Riyadh because of an Interpol order.
The journalist allegedly refused to comply with the group's requests, which included texting his son, and was then drugged, according to the newspaper.
He reportedly then told his killers, in his last words, to not keep his mouth closed because of his asthma, but then lost consciousness.
Khashoggi was suffocated with a bag put over his head, the Sabah reports, with the sounds of a scuffle allegedly picked up by the recording.
The newspaper also alleges the tape captured his alleged dismemberment at the hands of the forensic expert.
Reports of the existence of audio recordings from Khashoggi's death have been around since last year.
Turkish officials have publicly confirmed their existence and say they have shared them with international governments but it is unclear how the newspaper obtained them.
Almost a year on from his death, Khashoggi's body has not been recovered despite international pressure.
( With inputs from IANS )