WASHINGTON — A plea agreement hearing in federal court has been set for Tuesday in the case of an ex-CIA officer found with 303 gold bars worth $40 million at his home, according to court records.

David Rush, who has been accused of faking his lengthy professional record, has only formally been charged with one count of theft of public funds, accused of falsifying pay records. But two people familiar with the investigation have told NBC News that Rush is also accused of making up a false CIA program. Investigators believe there is likely more money or other items missing beyond what was seized by federal officials at his home, four people familiar with the investigation told NBC News.

Rush was placed on leave sometime before his arrest and eventually fired from the CIA. Court records show that the hearing Tuesday afternoon has been set before U.S. District Judge Michael Nachmanoff in Alexandria, Virginia.

A plea agreement would allow the government to avoid a lengthy trial which could bring further attention toward any mistakes the CIA made in the process and prevent the disclosure of additional information on the agency’s operations.

Rush has not yet entered a plea and has been held since his arrest. His attorney had no comment Monday. The prosecution and defense together had earlier requested additional time to work out a plea deal.

Rush’s case has also cast an unwelcome spotlight on the No. 2 at the Pentagon, Steve Feinberg, who had a close professional relationship with the former officer, sources told NBC News. Feinberg, through a Pentagon spokesperson, has denied the two had a close relationship.

Rush had worked on secret maritime programs at the Pentagon, NBC News reported in June. Deputy Defense Secretary Steve Feinberg was interviewed by the FBI as part of the investigation into Rush, but Feinberg has not been accused of wrongdoing and the bureau said in a statement he was not under investigation. There’s no indication Feinberg knew about Rush’s alleged fabrications. Several senior CIA officials were placed on leave over the management of Rush’s requests for money, NBC News reported in June.

The U.S. intelligence community’s inspector general is also investigating the circumstances that led to Rush’s arrest, which has raised questions among intelligence officials and U.S. lawmakers about how the CIA could have missed basic alleged falsehoods in Rush’s application, including about his academic and military records, NBC News reported last month.