A Turkish diplomatic source earlier said a joint Turkish-Saudi team would search the building - the last place Khashoggi was seen before he vanished on October 2.
The case has provoked an global outcry, with US President Donald Trump threatening "severe punishment" if it turns out Khashoggi was killed in the consulate and European allies urging "a credible investigation" and accountability for those responsible.
Saudi authorities have yet to give a clear explanation of Khashoggi's fate, while several countries - particularly Turkey, the USA, and the U.K - are pressing for the case to be cleared up as soon as possible.
Since self-exiled Saudi journalist Jamal Khashoggi walked into the Saudi Arabian consulate in Istanbul this month and vanished, his case has sparked worldwide intrigue and outrage and put leaders of his homeland on the defensive.
The statement was issued as worldwide concern grew over the writer who vanished on a visit to the Saudi Consulate in Istanbul over a week ago.
Riyadh has struck back at the allegations, calling them "lies" and threatening retaliation over any possible economic sanctions by USA or other western countries.
"There's something really awful and disgusting about that, if that was the case, so we're going to have to see", Trump said.
Turkish officials said that a Saudi hit squad killed Mr. Khashoggi and dismembered his body to smuggle it out of the country.
The case has provoked an worldwide outcry against Saudi Arabia, the world's top oil exporter, with more media and business executives pulling out of a planned investment conference there this month. "Nobody's seen it yet, so we do want to see it. we're going to be seeing it very soon". The third individual said the US government still doesn't know precisely what explanation the Saudis plan to give, but that the Saudis intend to admit "culpability".
"I have asked Secretary of State Mike Pompeo to get on a plane and go to Saudi Arabia. go to Turkey if necessary".
Companies and executives in other industries also appeared to distance themselves from the Saudis Monday. Saudi Arabia's riyal currency was still testing the boundaries of its peg at 3.7514 to the dollar - its weakest spot rate since June 2017.
On Monday, King Salman ordered an investigation into the case.
But Saudi Arabia has strongly denied the accusations, vowing to retaliate with "greater action".
"I don't think he should go", Rubio, a member of the Senate Foreign Relations Committee, told CNN's "State of the Union".