After critical talks in Riyadh Tuesday, Pompeo was expected in Turkey on Wednesday to meet Turkish Foreign Minister Mevlut Cavusoglu, the state-run Anadolu news agency said.
Saudi officials have called Turkish allegations that Saudi agents killed Khashoggi "baseless", but reports in USA media on Tuesday suggested the Saudis may acknowledge the writer was killed at the consulate, perhaps as part of a botched interrogation.
Pompeo's meetings in Turkey's capital, Ankara, were in sharp contrast to his talks a day earlier in Riyadh, where Saudi leaders repeated their denials that they had no knowledge of Khashoggi's fate after he entered the Saudi consulate in Istanbul earlier this month.
The New York Times and The Washington Post have reported, citing anonymous sources, that Saudi officials may soon acknowledge Khashoggi's slaying at the consulate but blame it on a botched intelligence operation.
U.S. media reported on Monday that the oil-rich kingdom is considering an admission that Khashoggi died after an interrogation that went wrong during an intended abduction.
Khashoggi hadn't been seen since he entered the consulate to obtain marriage license papers on October 2, and evidence points to Khashoggi having been killed and dismembered.
A Turkish Foreign Ministry official says Turkish authorities will search the residence of the top Saudi diplomat in Istanbul over missing journalist Jamal Khashoggi's disappearance.
A senior Turkish source revealed to MEE last week that Khashoggi was lured into the consul-general's office after he entered the consulate, before being dragged into another room and murdered. "It sounded to me like maybe these could have been rogue killers".
The U.S. State Department said on Tuesday that Secretary of State Mike Pompeo agreed with Saudi Arabia on the importance of conducting a "thorough, transparent, and timely" investigation of the disappearance of journalist Jamal Khashoggi. The Turkish official would not comment on the disposal method for the body.
Khashoggi, a familiar face on Arab talk shows, moved to Washington previous year fearing retribution for his criticism of Prince Mohammed, who has cracked down on dissent with arrests.More news: Green expected to play against Lakers in Warriors' final preseason game
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Saudi Arabia -Emirati led coalition destruction of Yemen and port blockade of Yemen's port Hodeida [in the pretext of routing Iran backed Houthi Rebels from controlling the country] has attracted global and relief agencies condemnation.
"We have asked for [audio and video] if it exists", Trump told reporters.
Both men were seen smiling and exchanging pleasantries ahead of a closed-door meeting to discuss the case of Khashoggi, a Saudi citizen and USA resident.
Concern that he also was a target drove Khashoggi into self-imposed exile in the United States last summer. Pompeo then met a smiling Prince Mohammed, the heir apparent to the throne of the world's largest oil exporter.
TRT World's Francis Collings has more from outside the Saudi consulate in Istanbul.
On Monday, however, Trump offered a different theory after speaking by telephone with King Salman.
Khashoggi told MEE that one of the crown prince's closest aides was the person who first told the journalist he had fallen out of favour with the royal court.
Trump has previously warned that the kingdom will face "severe punishment" from the US if it is determined that Saudi Arabia was responsible for Khashoggi's death.
Trump previously warned of "severe punishment" for the kingdom if it was found to be involved in Khashoggi's disappearance, which has spooked investors. The Sabah daily newspaper said investigators had wanted to search the building with luminol, a chemical which shows up any traces of blood.
Turkish officials have drip fed the media details of their investigation into Khashoggi's disappearance. On Sunday, the oil-rich kingdom suggested retaliation if the US were to impose strict measures.