Pompeo delivered the plan in person in October during a meeting in Riyadh with Saudi King Salman and bin Salman, a senior Saudi source who was familiar with Pompeo's talks with the Saudi leaders told MEE.
Khashoggi, a Washington Post contributor, was murdered on October 2 in what Saudi Arabia called a "rogue" operation, tipping the kingdom into one of its worst diplomatic crises and subsequently straining ties between Riyadh and Washington.
Qatar's Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani also said his country's relationship with America "has enabled us to confront so many regional and global challenges".
The journalist was murdered and his corpse dismembered inside the kingdom's Istanbul consulate.
His support has come despite the US Central Intelligence Agency's reported conclusion that Prince Mohammed very likely ordered the murder.
Riyadh prosecutors have announced indictments against 11 people, and are seeking the death penalty against five of them.
"It is time for old rivalries to end for the sake of the greater good of the region", Mr Pompeo said on Thursday in Cairo, where he laid out the Middle East strategy of US President Donald Trump's administration.
"So, he definitely has to mention Jamal Khashoggi, and he has to show that the United States is concerned with that, but I think they [the Trump administration] are much more on the same line [as the Saudis] - they don't want the Saudi crown prince [Mohammed bin Salman] to be hurt by this affair", said Majed.
It is not clear whether Pompeo will meet with Prince Mohammed in Riyadh on Monday.
Pompeo's visit came as human rights groups have been calling on Saudi Arabia to provide independent global monitors access to detained female prisoners amid mounting reports of torture and sexual harassment in Saudi prisons.
Acknowledging that Pompeo is set to seek an update on the Khashoggi murder investigation, al-Hathloul's sister, Alia al-Hathloul, noted that, "I am struck by what is not included in Mr. Pompeo's itinerary: the courageous women activists of Saudi Arabia, who are being held in the kingdom's prisons for seeking rights and dignity". But Prince Mohammed, whose right-hand aides were allegedly involved in the murder, was exonerated by prosecutors.
Pompeo refused on Sunday to comment on reports Washington had recently considered military action against Tehran.
He expressed gratitude to Qatar for hosting 13,000 USA soldiers at Al Udeid Air Base, going on to reiterate keenness on enhancing bilateral cooperation especially that Qatar will host the FIFA World Cup in 2022.
"We're all more powerful when we're working together", Pompeo said at a news conference. "Disputes between countries that have a shared objective are never helpful".
Later, speaking to a U.S. Embassy staff member in Qatar who said her job was moving to the UAE due to the boycott's effects, Pompeo was even more frank.
Bahrain, Egypt, Saudi Arabia and the United Arab Emirates began a boycott of Qatar in June 2017, alleging Qatar funds extremist groups and has too-cozy ties to Iran.
The United States, which at first appeared to back the boycott of Qatar, has so far been unsuccessful in trying to end the dispute. The proposed Middle East Strategic Alliance (MESA) has been dubbed an Arab Nato.
Pompeo arrived in the country on Sunday and signed several agreements with Qatari officials.