It remains unknown when Sherman's bill will be brought to the floor for a vote, but it will probably be after the new Democratic-controlled House of Representatives convenes on 3 January 2019.
Khashoggi disappeared after he entered the consulate on October 2 even as his fiancée Hatice Cengiz waited outside the building.
After more than two weeks of denials, Saudi Arabia acknowledged that the journalist had been killed in a fight inside the consulate.
His murder has led to a huge outcry across the globe.
If passed, the legislation could force Trump to submit a "123 Agreement", or a set of rules that make it legal for the United States to sell nuclear technology to another country, for congressional approval.
Trump Says Jim Acosta Video ‘Wasn’t Doctored’
Initially, the White House said Acosta placed his hands on an intern who attempted to take a microphone away from him. But Acosta initially refused to give up the microphone to anyone else and continued asking questions.
Congressman Brad Sherman's bill, titled "No Nuclear Weapons for Saudi Arabia Act of 2018", would not only prohibit the kingdom's construction of nuclear weapons from the material it buys from the U.S., it would also force Saudi Arabia to uphold a number of strict regulations to ensure that classified material regarding U.S. nuclear technology does not get leaked.
Mr Sherman's bill could block Saudi Arabia's plans to obtain nuclear technology from the US.
"We have not been able to get answers from Saudi Arabia about who ordered the murder", the minister said, stressing that President Recep Tayyip Erdogan is confident that King Salman Bin Abdulaziz did not order Khashoggi's murder.
A Republican is also set to back the bill when it's officially introduced in the next 10 congressional days.
Sources told Al Jazeera on Saturday that Turkish police ended the search for Khashoggi's body, but that the criminal investigation into the Saudi journalist's murder will continue.
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