The network said it will air the interview in full on Sunday evening.
The newspaper, for which Khashoggi is a columnist, cited anonymous officials as saying the recordings show a Saudi security team detained the writer when he went to the consulate on October 2 to pick up a document for his upcoming wedding.
Turkey has yet to publish any evidence of him being slain, though surveillance footage around the consulate shows a convoy of vehicles with diplomatic license plates leaving the Saudi Consulate for the consul's home in Istanbul a little under two hours after Khashoggi's arrival.
"He'd given it to her as she waited outside the consulate, telling her who to call if he didn't come out of the building", the report said, adding all the conversations of the Saudi executioners were recorded in this file".
Most US intelligence officials believe that Saudi Crown Prince Mohammad bin Salman had carried out an operation to murder Khashoggi, who wrote a series of columns criticising the kingdom country's regime in The Washington Post.
Foreign minister Jeremy Hunt has called on Saudi Arabia to explain what happened to Khashoggi.
Saudi officials have strongly denied any involvement in his disappearance and say that he left the consulate soon after arriving.
BBC weather forecast: Storm Callum sparks EVACUATION ALERT over 'life-threatening' flood
The Met Office is advising people to take caution as the weather could cause power cuts, travel disruptions and flooding. Forecasters are warning of more of the same over the weekend, although some parts of England will escape the worst.
Bahraini Prime Minister Prince Khalifa bin Salman Al Khalifa said during his meeting with Deputy Secretary of State John Sullivan that, "Supporting Saudi Arabia is a support for us because it represents all of us".
"There's a lot at stake, there's a lot at stake", Trump tells Stahl.
While Mr Trump said he would punish Saudi Arabia, he said he would not cancel arms sales to the kingdom in response, as a bipartisan group of USA senators have demanded.
"Human rights, freedom of information are essential rights and horrifying things have been reported and I am horrified", she told reporters in Bali where the International Monetary Fund is holding annual meetings.
Saudi and Turkish officials have not yet commented on the Sabah report.
President Donald Trump has said that he will go ahead with the $110 billion arms deal his administration negotiated with the Arab nation.
Stahl: Jamal Khashoggi, the journalist, the Saudi journalist.
According to her account, Khashoggi was not overly fearful before he entered Saudi consulate on October 2, although he did tell her to alert Turkish authorities if he did not return soon.
It was not clear whether United States officials have seen the footage or listened to the audio, but Turkish officials described their contents to their American counterparts, the newspaper said.