The visit was confirmed by a person familiar with the plans who spoke on condition of anonymity to discuss the private session.
Haspel's planned briefing follows criticism the White House did not allow the Central Intelligence Agency director to join an earlier meeting on Saudi policy conducted by Defense Secretary James Mattis and Secretary of State Mike Pompeo.
The CIA has not commented on the reports of Tuesday's briefing.
Khashoggi was killed in the Saudi consulate in Istanbul two months ago.
The veteran journalist was a strong critic of Prince Mohammed and had been resident in the United States, where he wrote about politics in Saudi Arabia and the Middle East for The Washington Post.
Sen. Bob Corker says a jury would find the Saudi crown prince 'in about 30 minutes.'
They overwhelmingly approved the resolution, 63-37, on an unexpectedly wide bipartisan vote. He was killed in what USA officials have described as an elaborate plot as he visited the consulate for marriage paperwork. Human rights groups say it is indiscriminately leading to civilian deaths.
Khashoggi, a Washington Post columnist and American resident, was murdered and dismembered minutes after he entered the Saudi consulate in Istanbul, Turkey on October 2 - allegedly on orders from Saudi Crown Prince Mohammed bin Salman.
The senators were not allow to disclose details of what they were told, but their reaction reinforced reports that the Central Intelligence Agency had accumulated substantial evidence that the crown prince was behind the murder. Trump has touted Saudi arms deals worth billions of dollars to the USA and recently thanked Saudi Arabia for plunging oil prices. In a column for the Wall Street Journal on Tuesday, Graham wrote that the killing and other moves by the Saudi regime showed "astounding arrogance entitlement" and disregard for worldwide norms.
"We're not quite there yet", Corker said ahead of the briefing.
"Some are saying there is no smoking gun", said Paul, referring to Mattis, the USA defence secretary, who said exactly that last week.
Brother of Australia cricketer arrested over fake terror 'hit list'
Mr Khawaja, who worked in the same department as Mr Nizamdeen, had been partly motivated by a "personal grievance" over a woman, police said.
FA Cup third round draw
The 20 Premier League clubs enter the frame, including holders Chelsea (ball number 12), as do the 24 members of the Championship.
National Football League investigating Hunt for second incident
It shows Hunt being restrained several times by friends before pushing a woman to the ground, where he proceeds to kick her. He took responsibility for the incident in an interview with ESPN over the weekend. "I want to apologize for my actions".