Riyadh has said Khashoggi left the consulate after his visit.
The English-language state broadcaster TRT World reported that Turkish officials believe the Saudis may have taken the consulate's CCTV footage with them when they returned to Riyadh.
Almost two hours later, the video shows two vehicles with diplomatic plates -a luxury black sedan and a black Mercedes VITO van- leave through the police barricades outside the consulate.
He is an outspoken critic of Saudi Arabia who has dared to defy Crown Prince Mohammed bin Salman, the kingdom's de facto ruler.
Sabah daily on Wednesday published the names and images of what it called the "assassination team" including a man called Salah Muhammed Al-Tubaigy whose name it said matched that of a lieutenant-colonel in the Saudi forensic department.
The Saudi government has refuted those allegations, saying that Khashoggi left the consulate shortly after he entered. Suggestions that Khashoggi was killed and his body then mutilated have gained wide circulation in the week since he vanished, and Turkish officials continue to insist he met a brutal fate when he stepped through the doors of the diplomatic mission.
Daily Sabah added that the Saudi crew arrived at the Saudi consulate general in Istanbul on 2 October and left the same evening despite making a hotel reservation for four days.
A surveillance video image surfaced on Tuesday showing Khashoggi walking into the consulate in Istanbul's upscale 4th Levent neighborhood.
Khashoggi's fiancée asks Trump to 'shed light' on his fate
The journalist's fiancée, Hatice Cengiz, wrote an op-ed on Tuesday expressing hope her man is still alive.
Security guards stand outside the Saudi Arabia's consulate in Istanbul, Tuesday, Oct. 9, 2018. Saudi Arabia may have agreed to the search in order to reassure its Western allies and the global community.
"If he is really murdered, it is not only Saudi-Turkish relations that will suffer, but the world's relations with Saudi Arabia will get significantly harmed", he said, echoing Erdogan in asking for an explanation from Riyadh.
Nine of the agents reportedly arrived on a private jet from the Saudi capital, Riyadh, at around 03:15 on the day Mr Khashoggi visited the consulate.
Khashoggi had sought to become a US citizen after living in self-imposed exile since a year ago, fearing repercussions for his criticism of the prince, Cengiz wrote.
Trump, who took his first overseas trip as US President to the kingdom and whose son-in-law Jared Kushner has close ties to Prince Mohammed, said Tuesday he had not yet talked to the Saudis about Khashoggi, "but I will be at some point", without elaborating.
Tuesday's statement from the Turkish Foreign Ministry's spokesman, Hami Aksoy, said Saudi authorities had notified Ankara that they were "open to cooperation" and would allow the consulate building to be searched.
The search will take place as part of the official investigation, which was being conducted "in an intense manner", he said without giving any date.
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