Saudi Arabia has denied the allegations.
Washington Post late on Tuesday published passport scans of the suspects allegedly involved in the journalist's killing, while another report detailed close links between the suspects and the powerful crown prince accused of ordering the murder. Pompeo said both Saudi Arabia and Turkey will complete their reports, which are being done separately, in a "timely fashion".
"They said, 'We have audio on this".
Answering a question on what would be the consequences for Saudi Arabia, Trump said: "Well, it'll have to be very severe".
"Unless the miracle of all miracles happens, I would acknowledge that he's dead", Trump said to The Times. "But we'll see what happens".
For now, the president said the United States is waiting for the results of several investigations but will then make a "very strong statement".
A source familiar with the Turkish investigation has told CNN that Saudi intelligence officer and former diplomat Maher Abdulaziz Mutreb played a "pivotal role" in the apparent assassination of Khashoggi.
Saudi officials deny any involvement in his disappearance.
"We do believe that between these two efforts a complete picture will emerge for what actually transpired here", Mr Pompeo said.
Meanwhile, Treasury Secretary Steve Mnuchin announced Thursday that he will not attend a previously scheduled Saudi investment conference.
Earlier on Thursday, senior government ministers from France, Britain and the Netherlands also withdrew from the Riyadh conference, joining a list of worldwide officials and business executives.
Meanwhile, human rights groups are banding together to call on the United Nations to set up an independent investigation, arguing Saudi authorities can not be trusted to deliver credible results, because they are investigating themselves.
Pompeo said he believes those combined efforts will produce "a complete picture" of what happened to Khashoggi, a Saudi journalist living in the USA who had been critical of the kingdom.
Turkish investigators have for a second time searched the Saudi consulate where Khashoggi disappeared, and also searched the consul's residence.
The Canadian official, speaking on condition of anonymity Thursday, declined to draw a direct link to recent events when asked why Canadians were skipping the summit - they said Canada is just not going.
Khashoggi's killers may have dumped his remains in Belgrad Forest adjacent to Istanbul, and at a rural location near the city of Yalova, a 90-kilometre (55 mile) drive south of Istanbul, the officials said.
Cavusoglu, like other Turkish officials, stopped short of revealing details of the investigation but vowed they would be shared in due course.
In Istanbul, a leaked surveillance photo showed a man who has been a member of the crown prince's entourage during trips overseas walking into the Saudi Consulate just before Mr Khashoggi vanished there.