The journalist had chose to leave his native Saudi Arabia for the United States in September 2017, but was lured to the embassy in Istanbul on in October 2018 to collect papers for his upcoming marriage.
According to a report by The New York Times, American intelligence agencies intercepted a 2017 conversation between the crown prince and his aide which revealed bin Salman's frustration over Khashoggi's criticism of the Saudi government and his refusal to return to the kingdom from the US. "It is also raising a number of worldwide implications which demand the urgent attention of the global community including the United Nations", she said.
It has arrested several senior Saudi officials, but the murder plunged the kingdom into one of its worst diplomatic crises.
Central Intelligence Agency officials ruled in November that Khashoggi's killing was likely ordered by bin Salman himself, however this report is the most direct evidence that ties the crown prince to the assassination.
Almost four months on, Khashoggi's body has not been recovered.
After Mr. Khashoggi's first visit to the consulate on Sept 28, Saudi planning included "the travel of the three teams that carried out the operation; the presence of a lookalike of Mr. Khashoggi who was seen leaving the consulate; the presence of a forensic doctor; the escape of the teams' members and, of course, the disposal of Mr. Khashoggi's body".
Callamard, a French human rights expert, is due to deliver a final report to the United Nations human rights council in June.
Saudi officials have denied MBS had any knowledge of the crime, however, and a trial opened earlier this month in the Gulf kingdom for 11 people suspected of being involved.
Khashoggi was strangled before being chopped into pieces by a hit team of 15 Saudis sent to Istanbul for the killing, according to Turkish officials, with local reports suggesting his remains were dissolved in acid.
Agnes Callamard, UN special rapporteur on executions, sought access to the Saudi consulate in Istanbul.
Ms Callamard was reporting on a week-long mission with her team of three experts to Turkey.
The statement did not say whether she had had access to the Saudi consulate in Istanbul, as she had requested.
"The Khashoggi murder is not an ordinary one".
Human rights groups and other observers also say the Saudi investigation into the killing has not met global standards and they have called for a thorough probe into the slaying.
Predicting little movement, a bipartisan group of senators on Thursday proposed a bill to cut off some weapons sales to Saudi Arabia including of tanks, long-range fighter jets and ordnance for automatic weapons. The prosecutor said authorities were seeking the death penalty for five of them.