He has not been seen since entering the building on 2 October.
Turkish officials have said they believe Khashoggi, 59, a critic of the Saudi leadership and a contributor to The Washington Post's Global Opinions section, was killed by a team of 15 Saudis flown in specifically to carry out the attack.
The fate of a dissident Saudi journalist who has disappeared in Istanbul, remains unknown.
On September 28, he visited the Saudi consulate in Istanbul to get marriage documents related to his planned marriage to his fiancé, a Turkish citizen, Hatice (Khadija) Cengiz.
Turkish President Tayyip Erdogan on Monday called on Riyadh to prove its claim that Saudi Arabian journalist Jamal Khashoggi, who has been missing since last week, left the Saudi consulate in Istanbul, while the Washington called on Saudi Arabia to support an investigation into his disappearance.
The New York Times account says its sources report the Saudis "had arrived to silence Mr. Khashoggi, but that it was not clear if the plan had been to bring him back to Saudi Arabia alive, and something went wrong, or if the intention was to kill him there".
A source described by Reuters as a "Turkish official" told the wire service, "The initial assessment of the Turkish police is that Mr. Khashoggi has been killed at the consulate of Saudi Arabia in Istanbul".
Khashoggi, who fled Saudi Arabia past year to go into self-imposed exile in the U.S., had always been critical of the Saudi regime.
Khashoggi hadn't lived in Saudi Arabia since he moved to the United States past year.
The image released by the Post bore a date and date stamp. He said he believes Turkish officials soon will announce the findings of their investigation.
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The door Mr Khashoggi walked through appeared to be the main entrance of the consulate in Istanbul's 4th Levent neighbourhood. The consulate insists the writer left its premises, contradicting Turkish officials.
It's unclear which camera the footage came from or who operated it. However, they have failed to provide any proof that the journalist left.
"If the reports of Jamal's murder are true, it is a monstrous and unfathomable act", the Post's editorial page editor Fred Hiatt said in a statement.
Hiatt added that the "idea of a government luring one of its own citizens onto its own diplomatic property in a foreign country to murder him for the peaceful expression of his views would be unimaginable". Writing as a columnist for the Washington Post, articles took aim at the country's conduct in Yemen's civil war, and the crushing of political dissent at home by heir apparent Crown Prince Mohammad bin Salman.
"He entered the general consulate himself, and if he has entered by himself and if he did not exit it, of course this should be proven by the general consulate", Erdogan said at a news conference in Budapest.
"Do you not have cameras and everything of the sort?" Then why do you not prove this?
"State Department senior officials have spoken with the Kingdom of Saudi Arabia through diplomatic channels about this matter", he said. Both spoke on condition of anonymity as the investigation was ongoing.
The planes belonged to a company based in Saudi Arabia which has links to the state.
Officials in Saudi Arabia did not immediately respond to a request for comment. "We are aware of the latest reports and are working urgently to establish the facts, including with the government of Saudi Arabia".