The top Democrat on the Senate Judiciary Committee, Dianne Feinstein of California, said Thursday that she has referred a letter concerning Supreme Court nominee Brett Kavanaugh to federal authorities.

"I have received information from an individual concerning the nomination of Brett Kavanaugh to the Supreme Court," Feinstein said. "That individual strongly requested confidentiality, declined to come forward or press the matter further, and I have honored that decision. I have, however, referred the matter to federal investigative authorities."

Feinstein's announcement came shortly after the committee set a date to vote on Kavanaugh's nomination over the objections of Democrats.

Later Thursday, The Washington Post, citing a person familiar with the matter, reported that the FBI did not plan to open an investigation. The law enforcement agency included the letter as an update to Kavanaugh's background check provided to the White House, a spokesperson for the bureau told CNBC.

Feinstein's disclosure came during the last weeks of Kavanaugh's confirmation process, and followed a report Wednesday night in the investigative news outlet The Intercept that first disclosed the existence of the letter. According to the outlet, the letter is rumored to include details about an incident involving Kavanaugh that took place during his time at Georgetown Preparatory School in Maryland.

The incident involved possible sexual misconduct between Kavanaugh and a woman who was also in high school at the time, two officials familiar with the matter told The New York Times. CNBC has not independently confirmed the contents of the letter.

Sen. Dick Durbin, D-Ill., told Buzzfeed News earlier in the day that the letter had been referred to the FBI. A source familiar with the matter confirmed Durbin's comments to CNBC Thursday.

The letter was reportedly written by someone affiliated with Stanford University. It was sent to Rep. Anna Eshoo, who represents California's 14th District, before being passed along to Feinstein.

A spokesperson for Eshoo's office declined to comment on the matter.

"Our office has a confidentiality policy regarding constituent casework," the spokesperson told NBC News.

Feinstein has not shared details about the letter beyond her statement Thursday, and no other senators on the Judiciary Committee have been permitted to see it, according to reports.

The woman who is the subject of the letter is reportedly represented by Debra Katz, a whistleblower attorney who has been described as "Washington's top attorney for women who want to fight back" in a profile in the magazine The Washingtonian.