The bill would come as a huge blow for Saudi who just last Monday launched a project to build the country's first nuclear research reactor.
The investigative team looking into the disappearance of Saudi journalist Jamal Khashoggi has discovered traces of hydrofluoric acid and other chemicals inside a well at the Saudi consul general's home in Istanbul, Al Jazeera reports citing a source in the Turkish attorney general's office.
Many people in the USA now want to see the relationship between Washington and Riyadh terminated.
Mr Sherman's bill could block Saudi Arabia's plans to obtain nuclear technology from the US.
Mr Sherman told Vox: "I don't think this bill would've passed prior to the events in Istanbul".
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.More news: Tens of thousands flee fast-moving Northern California fire
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"The new Saudi totalitarianism, which requires complete subservience and loyalty to the crown prince, has culminated in the scandal of Khashoggi's murder", Al-Rasheed wrote.
Although the kingdom insists that bin Salman had nothing to do with the murder, many observers believe he personally ordered the hit job.
Mohammed Bin Salman (MbS) and Saudi Arabia have changed their official position on what happened to the journalist in the face of worldwide pressure.
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 United States, it would also force Saudi Arabia to uphold a number of strict regulations to ensure that classified material regarding USA nuclear technology does not get leaked.
Turkish President Recep Tayyip Erdogan repeated his assertion that Saudi Arabia knew who had killed Khashoggi.