Khashoggi, who was living in Virginia at the time of his disappearance, traveled to Istanbul and entered the Saudi consulate there to obtain a document he needed to marry his fiancee.
President Trump, who earlier this week dispatched Secretary of State Mike Pompeo to Saudi Arabia and Turkey, said he wanted to find out what happened before taking any action against Saudi Arabia, a key U.S. ally in the Middle East.
Karen Attiah, the Global Opinions editor at The Post, wrote a note at the top of Khashoggi's newest article.
Over the past few days, Mr Trump has raised the possibility of "rogue killers" being behind the journalist's disappearance.
The newspaper said Saudi Consul General Mohammed al Otaibi could be heard on the tape, telling those allegedly torturing Khashoggi: "Do this outside; you're going to get me in trouble". Khashoggi had left the country a year ago amid the rise of Prince Mohammed, whom he wrote critically about in the Post.
Following a search by a Turkish forensics team, President Recep Tayyip Erdogan said that some "toxic materials" in the consulate had been "painted over".
"There seems to be clear evidence that Khashoggi entered the Consulate and has never been seen since, the onus is on the Saudi authorities to reveal what happened to him from that point onwards", she said.
The leaks, a lot of them reported in local pro-government newspapers in Turkey, may provide a clearer picture of what happened over two weeks ago when Khashoggi entered the Saudi consulate to obtain documents related to his upcoming marriage to a Turkish woman.
Adding to the picture of Saudi influence potentially weighing on American decision-making about Khashoggi, US media reported that US$100 million for Washington's stabilisation efforts in Syria was deposited by the kingdom as Pompeo arrived in Riyadh.
Pompeo had previously expressed confidence that the Saudi probe into Khashoggi's disappearance would be "thorough, complete and transparent". "If it exists we have asked for it", Trump told reporters in the Oval Office.
"You know we need Saudi Arabia in terms of our fight against all of the terrorism, everything that's happening in Iran and other places".
Al-Otaibi returned to Saudi Arabia on Tuesday before his residence in Istanbul was searched by police on Wednesday and Thursday.
Turkish officials have accused Saudi Arabia of killing Khashoggi, who was often critical of the Saudi government in his writing.
The paper said a Saudi team immediately grabbed the journalist after he entered the consulate, cutting off his fingers and later decapitating him.
Mnuchin sent a tweet on Thursday saying that after meeting with President Donald Trump and Secretary of State Michael Pompeo he decided not to participate in the Future Investment Initiative, an event organized by Crown Prince Mohammed bin Salman.
Mr Mutreb, perhaps a bodyguard, has been photographed emerging from planes with Prince Mohammed on recent trips to Madrid and Paris, the newspaper reported.
On Wednesday, German Foreign Minister Heiko Mass called off his scheduled visit to Riyadh and asked Saudi officials to "fully cooperate" in the investigation.
The family of missing Saudi journalist Jamal Khashoggi has rejected all attempts to use its name to target Saudi Arabia, according to reports.