One of those two individuals said he was told by those close to the Saudi leadership that the kingdom will claim that rogue operatives killed Khashoggi during an interrogation or a rendition attempt that went horribly awry.
The controversy has troubled Saudi's traditional Western allies - who are key arms suppliers to the kingdom - and also undermined efforts by Mohamed bin Salman to present himself as a modernising ruler.
"There's something really bad and disgusting about that, if that was the case, so we're going to have to see", Trump said.
Mr Trump addressed snatched questions from reporters over helicopter engine noise at the White House, describing King Salman's denial as "very, very strong".
President Donald Trump initially made it clear that whatever the outcome of the inquiry into the disappearance of Khashoggi, the USA would not forgo billions of dollars in arms deals with Saudi Arabia. The president added in a tweet that he is dispatching Secretary of State Mike Pompeo "immediately" to meet with the King in person. Certain areas of the consulate were to remain off-limits, although officials would be able to inspect surveillance cameras, Turkish media reported.
House Minority Leader Nancy Pelosi (D-CA) floated an accusation that a personal financial transaction with Saudi Arabia has resulted in a softer response from President Donald Trump in the case of missing journalist Jamal Khashoggi.
Khashoggi, a Saudi national and USA resident who has been a vocal press critic of Saudi Prince Mohammed bin Salman, has not been seen since entering the Saudi consulate in Istanbul on October 2. Surveillance footage captured him entering through the consulate's main entrance, but he was never seen leaving. "We're going to get to the bottom of it, and there will be severe punishment".
The king phoned Erdogan "to thank the president for welcoming the kingdom's proposal to form a joint working group to discuss the disappearance of Saudi citizen Jamal Khashoggi". A spokesman for JPMorgan confirmed chief executive Jamie Dimon will no longer attend, but declined to say why.
Saudi Arabia had earlier denied killing Khashoggi and denounced such assertions as "lies", saying he left the building shortly after entering.
Already, worldwide business leaders are pulling out of the kingdom's upcoming investment forum, a high-profile event known as "Davos in the Desert", and the sell-off on Riyadh's Tadawul stock exchange showed that investors are uneasy.
A joint Saudi-Turkish team arrived at the consulate on Monday in Istanbul's upscale 4th Levent neighbourhood, as journalists filmed and shot photographs of their arrival.