Saudi Arabia late a year ago indicted 11 people for the killing at the Kingdom's consulate in Istanbul in October.
"The Custodian of the Two Holy Mosques King Salman bin Abdulaziz and the Crown Prince Mohammed bin Salman are considered and regarded as guardians to all Saudis".
"Currently, the trial is taking place and no settlement discussion had been or is discussed", Salah said in a statement he posted on his Twitter account on Wednesday.
The posting represented the first statement from the family since The Washington Post reported this month that all four of Khashoggi's adult children have been given multimillion-dollar homes in the kingdom and are receiving monthly payments exceeding $10,000 apiece.
Saudi Arabia's public prosecutor has charged 11 people over his murder.
"There are no friends or consultants or any third party authorized to speak on our behalf or claim to be a source of information except us, Jamal's children and Mr. Motasem Khashoggi our attorney", Salah Khashoggi said.
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"Acts of wisdom and generosity arise from high morals and humanity and are not an admission of guilt or error".
He went on to say that people are eager to get news about his father and the family will be "sharing developments as soon as they are legally admissible and allowed".
A bipartisan chorus of USA lawmakers has called on the White House to harden its stance toward Saudi Arabia after Khashoggi was killed at the Saudi consulate in Istanbul.
But senators from both parties have demanded the White House be more forthcoming about intelligence gathered on what happened to Khashoggi, and have signaled they may back broader sanctions against Saudi Arabia.
The section in question "provides that, in cases where the Secretary of State has credible information that officials of foreign governments have been involved in significant corruption or gross violations of human rights, those individuals and their immediate family members are ineligible for entry into the United States".
The State Department previously revoked the visas of almost two dozen Saudi officials and froze the assets of 17 others.