"I don't want to hear the tape, no reason for me to hear the tape", Trump told Fox News in a pre-recorded interview to be broadcast on Sunday. "Because it's a suffering tape, It's a bad tape".
Trump on Saturday told reporters that the USA would release "a very full report" on the matter as early as Monday.
About the killing itself, Trump told presenter Chris Wallace: "It was very violent, very vicious and bad".
But despite Saudi denials, American intelligence agencies have concluded that the crown prince ordered Khashoggi's killing, one U.S. official familiar with the assessment told the Associated Press.
Saudi Arabia says Khashoggi was killed as the result of a rogue operation.
Fox interviewer Chris Wallace asked Trump whether he would go along with moves in Congress to cut off US involvement in the Saudi-led war in Yemen or halt arms sales to Riyadh, but Trump said it depends. Are we really doing anything to punish them?
Weeks later, the Saudi government acknowledged that he was killed inside the consulate and last Thursday, the kingdom's attorney general that he would seek the death penalty for five of the 11 suspects charged in connection with the journalist's death.
Republican Senator Jeff Flake of Arizona, a frequent critic of Trump who sits on the Senate Foreign Relations Committee, said on CNN's "State of the Union" that the USA response should not be driven by its ties to Saudi Arabia.
Trump added he did not want to point the finger at Prince Salman, but noted that people close to the de-facto leader may have been involved.
After the killing, one of the team members was was heard, on recording by a listening device planted in the consulate by the Turks, telling a close adviser to the crown prince, Saudi al-Qahtani, "tell your boss" it's done.
"Well, will anybody really know?"
Others familiar with the case caution that while it's likely that the crown prince was involved in the death, there continue to be questions about what role he played.
"They may have taken out Khashoggi's dismembered corpse inside luggage without facing problems due to their diplomatic immunity", broadcaster CNN Turk quoted Akar, who was speaking at a panel as part of an worldwide conference in Halifax, Canada. "And I have no intention of working with him ever again", he said on NBC's "Meet the Press".
A still image taken from CCTV video and obtained by TRT World claims to show Saudi journalist Jamal Khashoggi, highlighted in a red circle by the source, as he stands with his fiancee Hatice Cengiz outside the Saudi Arabia's Consulate in Istanbul. There's no reason for me to hear it.
Investigators believe the operation that resulted in Khashoggi's death would not have been possible without bin Salman's knowledge given his government control, the senior US official added.More news: USA utility stocks slump as California wildfires leave hundreds missing
More news: Djokovic crushes Zverev at ATP Finals
More news: Manchester United duo set for January exit