Christine Blasey Ford, the woman accusing Supreme Court nominee Brett Kavanaugh of sexually assaulting her at a party 36 years ago, is willing to testify next week in front of the Senate Judiciary Committee, US media reported on Thursday.

Judge Brett Kavanaugh testifies during the second day of his US Senate Judiciary Committee confirmation hearing to be an Associate Justice on the US Supreme Court, on Capitol Hill in Washington, DC, September 5, 2018. (Photo: AFP)

Blasey Ford's lawyers have told the committee she cannot appear at its hearing scheduled for Monday, calling the date Republicans set "arbitrary," according to The Washington Post and The New York Times.

Both cited an email the lawyers sent to the committee seeking to negotiate a new date for the hearing, after committee chairman Chuck Grassley set a deadline of Friday morning to agree to appear on Monday.

The Monday date "is not possible and the committee's insistence that it occur then is arbitrary in any event," Blasey Ford's lawyers said.

"As you are aware, she has been receiving death threats, which have been reported to the Federal Bureau of Investigation, and she and her family have been forced out of their home," it said.

"She wishes to testify, provided that we can agree on terms that are fair and which ensure her safety."

They asked to hold discussions with the committee to set up a new date and conditions for the hearing.

"Her strong preference continues to be for the Senate Judiciary Committee to allow for a full investigation prior to her testimony."

Blasey Ford has been reluctant to testify since she came forward Sunday with her bombshell allegation, which threatened to derail the nomination of Kavanaugh, who would deliver a momentous conservative shift to the powerful high court.

Instead she has sought to have the FBI investigate the incident as part of its official background check on the nominee.

But, with Kavanaugh denying the accusation and Blasey Ford so far unable to produce witnesses on her own behalf, Grassley and the White House have pressed for her to testify soon in hopes they can get past the controversy and quickly get Kavanaugh approved.

Republicans fear if the nomination is delayed any further, it could be endangered by a possible Democratic sweep of the looming congressional midterm elections in seven weeks.