Prince Mohammed reportedly said this in a phone call with the White House after Khashoggi disappeared but before Saudi Arabia admitted killing him, reports BBC.
Saudi Arabia has denied the reports in the Washington Post and New York Times.
Khashoggi, a Saudi national working for the US press, was a well-known critic of his home country's rulers.
His body has not yet been found, but Turkey, the US and Saudi Arabia have all agreed that he was killed at the Saudi consulate in Istanbul on 2 October.
Saudi Arabia denies its royal family was involved and says it is "determined to find out all the facts".
Late last month, Prince Mohammed said that "the crime was painful to all Saudis".
What was said in the phone call?
During the call with President Donald Trump's son-in-law Jared Kushner and National Security Advisor John Bolton, Prince Mohammed said Khashoggi had been a member of the Muslim Brotherhood, a transnational Islamist organisation, the Washington Post reported.
The phone call is reported to have taken place on 9 October, a week after Khashoggi disappeared.
Prince Mohammed also reportedly urged the White House to preserve the US-Saudi alliance.
In a statement to the newspaper, Khashoggi's family denied he was a member of the Muslim Brotherhood and said the murdered writer had himself denied this repeatedly in recent years.
"Jamal Khashoggi was not a dangerous person in any way possible. To claim otherwise would be ridiculous," the statement said.
What has the investigation found so far?
There is still no consensus on how Khashoggi died.
He entered the consulate to sort out documents for his marriage to his Turkish fiancée, Hatice Cengiz.
On Wednesday Turkey said he was strangled immediately after entering the consulate and his body dismembered "in accordance with plans made in advance".
Turkish media had previously quoted sources as saying Khashoggi had been tortured.
Saudi Arabia has changed its account of what happened to Khashoggi.
When he first disappeared, it said Khashoggi had walked out of the building alive. It later admitted he had been murdered, saying the killing was premeditated and a result of a "rogue operation".
It has arrested 18 suspects, who, it says, will be prosecuted in Saudi Arabia. Turkey wants the suspects to be extradited.
Turkey has steered away from publicly blaming Saudi Arabia for the killing.
President Recep Tayyip Erdogan spoke to Saudi King Salman last week, and the two agreed to continue co-operating in the investigation.
What do other countries say?
Saudi Arabia has faced backlash over the death, including from its allies, who have called for answers.
President Trump has said he is "not satisfied" with the Saudi account. However, he also said he was unwilling to sacrifice lucrative arms deals with the country.
On Thursday US secretary of State Mike Pompeo said it would be a "handful more weeks" before the US knew enough to impose sanctions on individuals involved in Khashoggi's killing.
Mr Pompeo told a local radio station in St Louis that the US had "deep and long-term strategic relationships" with Saudi Arabia and said "we intend to make sure that those relationships remain intact".
US activists have launched a petition, calling for a section of road near the Saudi embassy in Washington to be renamed Jamal Khashoggi Way.
On Wednesday, France's Foreign Minister Jean-Yves Le Drian said Khashoggi's death was a "crime" and "odious".
He said France was not "dependent on our economic relations with Saudi Arabia" and the country would impose sanctions, but no details were given.
UK Foreign Secretary Jeremy Hunt also said it was an appalling act, adding that it had "possibly" given the US and the UK a chance to put new pressure on Saudi Arabia over other issues.
Earlier, the US called for a swift cessation of hostilities in Yemen, where a Saudi-led coalition has been fighting local Houthi rebels.