The CNN report comes hours after President Donald Trump told reporters that King Salman of Saudi Arabia strongly denied his government had any involvement in Khashoggi's disappearance and said "rogue killers" could be responsible.
Saudi Arabia has pledged to economically retaliate for any US punitive action.
"It has been 13 days since the event, so surely proving some of the evidence might be hard, but we believe we will obtain evidence", a Turkish official told Reuters. "The denial was very, very strong", Trump told reporters.
But Trump, who has frequently boasted about his business ties with the kingdom, suggested during the CBS interview that ending US arms sales to Saudi Arabia would not be an option, saying, "I don't want to hurt jobs". He went into self-imposed exile in the United States following the ascension of Prince Mohammed, now next in line to succeed his father, the 82-year-old King Salman.
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Turkish officials say they fear a Saudi hit team killed and dismembered the Washington Post contributor.
Two of the officials said the search could take place as early as Monday afternoon. But he disappeared when there is video evidence of him being at the Saudi consulate.
Britain, Germany and France have jointly called for a "credible investigation, ' Egypt has backed Saudi Arabia and warned of "false claims" against its ally and Australia's foreign minister has said she is 'deeply concerned".
Until now, Riyadh has not allowed Turkish investigators to search the consulate - officially Saudi territory - with reports both sides were at odds over the conditions.
Sources told CNN that the Saudis are preparing a report that will acknowledge that the death of Khashoggi, a former Saudi royal insider who became a critic of Crown Prince Mohammed bin Salman, was the result of an interrogation that went wrong.
Turkish official: New evidence Saudi writer slain in consulate
But it was delayed because no Saudi official was present for the joint investigation, the Turkish official added. In contrast to the president's cautious words, Graham offered a fiery critic of Saudi Arabia.
"It's either going to be a partial admission of guilt while trying to absolve the top level, or they'll say they haven't found anything", said Steffen Hertog, an associate professor at the London School of Economics.
The king said Turkey and Saudi Arabia enjoy close relations and "that no one will get to undermine the strength of this relationship", according to a statement on the state-run Saudi Press Agency.
The White House is brushing aside threats by Saudi Arabia that it may economically retaliate for any US punitive action imposed over the suspected murder of journalist Jamal Khashoggi, pledging a "swift, open, transparent investigation" into his disappearance.
In a "60 Minutes" interview that aired on Sunday, Trump said there would be consequences if it turned out Saudi Arabia had anything to do with Khashoggi's mysterious disappearance.
Turkey and Saudi Arabia work together on some common issues and share business interests, but also have a good deal of political bad blood. "And this is very important to get to the bottom of it".
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