Jamal's son Salah Khashoggi said that no such settlement was discussed now or before, adding that trial for his father's murder is underway.
After offering shifting accounts of what transpired, and under intense worldwide and Turkish pressure, the kingdom eventually settled on the explanation that Khashoggi had been killed by Saudi agents in an operation masterminded by two of the crown prince's top aides, who have since been removed from their posts. His body has not been recovered.
The White House said on Tuesday that U.S. President Donald Trump and Saudi Crown Prince Mohammed bin Salman Al Saud had talked over phone on issues regarding regional security, Iran and human rights.
Bin Salman has denied any knowledge of the killing or its botched cover-up, which Riyadh has described as a "rogue operation".
While ruling out a "settlement", the family statement did not, however, explicitly deny receiving compensation.
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According to the Post, the payments to his four children - two sons and two daughters - "are part of an effort by Saudi Arabia to reach a long-term arrangement with Khashoggi family members, aimed in part at ensuring that they continue to show restraint in their public statements".
The US Senate on Wednesday (local time) voted to confirm John Abizaid as the new ambassador to Saudi Arabia, a position that was lying vacant since 2017.
The Khashoggi murder has sparked worldwide outcry and calls to end arms sales to Saudi Arabia, which leads a regional military campaign battling Yemeni rebels linked to Iran.
The State Department previously revoked the visas of almost two dozen Saudi officials and froze the assets of 17 others.