Mr Khashoggi was last seen visiting the Saudi consulate in Istanbul last week, and Turkey says he may have been murdered there.
Saudi Arabia denies the suggestion.
Earlier today, US President Donald Trump said he had not yet spoken to Saudi officials about the journalist’s disappearance.
“I have not. But I will be at some point,” he told reporters. “I know nothing right now. I know what everybody else knows – nothing.”
Turkey says it will conduct a search of Saudi Arabia’s consulate in Istanbul.
Saudi Arabia’s foreign ministry said the country was “open to co-operation” and a search of the building could go ahead as part of the investigation.
It says the journalist left the consulate shortly after arriving, while Turkey says he was not seen leaving the building.
The country has demanded Saudi Arabia prove he left, while not providing evidence to support the claim he was killed inside.
Who is Jamal Khashoogi?
A critic of Crown Prince Mohammed bin Salman, Mr Khashoggi was living in self-imposed exile in the US and writing opinion pieces for the Washington Post before his disappearance.