Dr Ford claims Kavanaugh and a friend attempted to rape her at a high school party in the 1980s. He has denied the allegation, as has the White House, claiming there are numerous holes in her story.
Despite the reported conclusion by the White House, Senators conducting the confirmation hearing for Kavanaugh's nomination to the highest court in the country will still ultimately determine his future.
It is expected the committee will review the findings of the investigation on Thursday local time.
Despite the new FBI investigation, Democrats claim the White House imposed too many restrictions on its scope, which narrowed how thorough it could be.
Investigators did not interview Dr Ford — something her lawyers have claimed shows a lack of impartiality.
The allegations have ignited fury across the US, including protests from women's groups and sexual assault survivor advocates.
They say Dr Ford has been attacked for coming forward and insist her account of events should be believed.
Division only grew when Donald Trump mocked the psychology professor's testimony at a fiery rally in Mississippi earlier this week.
The audience laughed as Trump ran through a list of what he described as holes in Dr Ford's testimony before the Senate Judiciary Committee.
"How did you get home? 'I don't remember,"' Trump said at the rally in Southaven. "How did you get there? 'I don't remember.' Where is the place? 'I don't remember.' How many years ago was it? 'I don't know. I don't know. I don't know."'
Imitating Dr Ford, he added, "But I had one beer — that's the only thing I remember."
Dr Ford's lawyer Michael Bromwich called Trump's attack "vicious, vile and soulless."
"Is it any wonder that she was terrified to come forward, and that other sexual assault survivors are as well?" Bromwich tweeted. "She is a remarkable profile in courage. He is a profile in cowardice."
A massive coalition of Christian churches, attended by 40 million people, have said they want Kavanaugh to withdraw his nomination.
The National Council of Churches said the conservative jurist has "disqualified himself".
The group said in a statement that at last week's dramatic Senate Judiciary Committee hearing, he showed "extreme partisan bias," demonstrating he lacks the temperament to join the high court.