The Saudi government could not be reached immediately for comment on the CNN report. The network cited two anonymous sources, one of whom cautioned the report could change.
Trump sent Pompeo to meet with the Saudi king in Riyadh on Monday and said Pompeo may travel to Turkey as well. But Trump has said he is wary of halting US military sales to Saudi Arabia over the incident.
Trump dispatched Secretary of State Mike Pompeo to meet King Salman over the case that has strained the Americans' relationship with the Saudis, carefully cultivated by the US president.
Mr Khashoggi, a critic of the Saudi government who has written for the Washington Post, was last seen walking into the consulate on 2 October. "If the Saudis cut down the oil their country produces by a significant amount, this could cause a lot of tension on the oil markets and cause oil prices to jump very quickly in a very short amount of time, which would harm western economies", he said.
"We don't know for sure what happened and I would say that Khashoggi has also been really critical of the Iranians, that we have - you know the Saudis are - they are among the gulf nations who have together tried to be moderate Arabs in the fight against radical Islam..."
The United States and Saudi Arabia are now discussing the measures that can be taken if it turns out journalist Jamal Khashoggi was killed by Saudi agents while visiting the country's consulate in Istanbul earlier this month.
The Saudi government has described the allegations as "baseless", but have offered no evidence that Mr Khashoggi left the consulate.
Abrazos de tres minutos en la frontera de México
Posteriormente, la Patrulla Fronteriza anunció la construcción de un muro de acero, en un tramo de cuatro millas en El Paso, Texas .
Similar campaigns trended on social media in Saudi Arabia and the United Arab Emirates.
Trump called Pompeo on Sunday night and asked him to have face-to-face meetings with the Saudi leaders, State Department spokeswoman Heather Nauert said.
Trump added, "We're going to get to the bottom of it, and there will be severe punishment". "He may not", Trump said during a visit to Alabama.
The search came after Turkish President Recep Tayyip Erdogan and King Salman also had their first telephone talks since the controversy erupted, in what appeared to be a conciliatory conversation according to official readouts.
"The king has ordered the public prosecutor to open an internal investigation into the Khashoggi matter based on the information from the joint team in Istanbul", an official quoted Reuters.
A growing number of company executives as well as media organisations continued to pull out of the event, known as the "Davos in the Desert", set for October 23 to 25.