Khashoggi was killed on 2 October in the Saudi consulate in Istanbul.
Officials told US media such an operation would have needed the prince's approval. But Saudi Arabia maintains it was a "rogue operation".
"They didn't conclude," Mr Trump said when asked about the CIA's evaluation by reporters at Mar-a-Lago in Florida.
His comments on Thursday came as the Saudi crown prince began a regional tour of the Middle East, starting with the United Arab Emirates - his first official trip abroad since Khashoggi was killed.
The crown prince is also expected to participate in a G20 meeting of world leaders in Buenos Aires at the end of the month that will be attended by leaders from the US, Turkey and a number of European countries.
Meanwhile, France has announced that it is imposing sanctions on 18 Saudi nationals - the same individuals targeted with sanctions by the US, UK and Germany - allegedly linked to the Khashoggi murder.
Their list of individuals does not include the crown prince, a spokesperson for the French ministry of foreign affairs said.
"They have feelings certain ways. I have the report, they have not concluded, I don't know if anyone's going to be able to conclude the crown prince did it," Mr Trump told reporters in Florida.
"But whether he did or whether he didn't, he denies it vehemently. His father denies it, the king, vehemently," he added.
His statement said: "[It] could very well be that the crown prince had knowledge of this tragic event - maybe he did and maybe he didn't!"
The president has repeatedly stressed the importance of Saudi Arabia to the US following the killing, calling the kingdom a "steadfast partner" that has agreed to invest "a record amount of money" in the country.
Saudi Arabia says claims that the crown prince may have ordered the Khashoggi killing are false and maintains that he knew nothing about it.
The Gulf kingdom's public prosecutor earlier said that Khashoggi was killed inside the consulate as a result of a "rogue operation" on the orders of an intelligence officer.
Khashoggi was given a lethal injection after a struggle. His body was then dismembered inside the consulate in Istanbul and the body parts were handed over to a local "collaborator" outside the grounds, the prosecutor said.
He said investigations had "revealed that the person who ordered the killing was the head of the negotiations team", but did not identify any of the 11 people charged with the murder.