Wall Street Journal reported late Wednesday night that the White House has concluded that there was no corroboration found in the sexual misconduct allegations made against Kavanaugh in recent weeks, according to people "familiar with the matter".
One wildcard in the GOP's plan is President Trump, who at a campaign rally Tuesday mocked the testimony of Christine Blasey Ford - who told Senate lawmakers that Kavanaugh sexually attacked her in 1982 - causing concern among key Republicans in the Senate whose votes on Kavanaugh are crucial.
Senators delayed a vote on Kavanaugh so the FBI could conduct a background investigation into the allegations of sexual misconduct against him.
The FBI's report will be available at a sensitive compartmented information facility, or SCIF, in the Capitol Visitor Center, a secure room designed for senators to review sensitive or classified material, two Senate officials said.
If he joins the Supreme Court, Judge Kavanaugh, 53, would be expected to tilt its ideological balance in favour of conservatives. Agents should also interview Ford's friend Leland Keyser, although she has said that she doesn't recall the event.
Republicans hold a 51-49 majority in the Senate and a simple majority is needed to advance his nomination. McConnell said on Tuesday that the report should not become public.
"The Constitution tasks the Senate, not the media or the Federal Bureau of Investigation, with providing advice and consent for Supreme Court nominees", he said, calling it "disappointing" that Ms. Blasey Ford showed documents to The Washington Post but has refused to provide them to lawmakers.
And speaking at an event hosted by The Atlantic magazine, Trump ally Senator Lindsey Graham of SC said he "didn't particularly like" the president's remarks, adding, "I would tell him, knock it off".
Kavanaugh has denied the accusations by all three women.
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McConnell, R-Ky., claimed on the Senate floor that the protesters were "part of the organized effort" to derail Kavanaugh's nomination and said, "There is no chance in the world that they're going to scare us out of doing our duty".
She said Mr Kavanaugh was drunk and had pinned her onto a bed, tried to remove her clothing and put his hand over her mouth when she screamed.
Republican Senate Majority Leader Mitch McConnell wants a final Senate vote on Judge Kavanaugh's nomination on Saturday.
The letter also says Kavanaugh gave "intemperate, inflammatory" responses and was "discourteous" to senators. Heidi Heitkamp of North Dakota, who is undecided on Kavanaugh, trailing her Republican challenger Kevin Cramer by eight points. "'I don't know, but I had one beer!'"
President Trump was cheered on by a crowd of Republican faithful in MS yesterday as he mimicked Dr Ford's responses to questions at last week's Senate hearing and joked about her inability to remember details surrounding the night of her alleged attack. I don't know. I don't know. 'How did you get there?' I don't remember.
The FBI did not include any conclusions as to whether Ford or Kavanaugh was telling the truth.
The White House insisted Trump was merely restating facts, although Ford had conclusively said the assault happened upstairs and remembered many other details vividly.
Also interviewed was Tim Gaudette, a high school classmate of Kavanaugh.
"Instead of trying to sort out with reason and care the allegations that were raised, Judge Kavanaugh responded in an intemperate, inflammatory, and partial manner, as he interrupted and, at times, was discourteous to questioners", the letter goes on.