Back in 1991, however, the FBI did investigate sexual harassment claims against then-Supreme Court nominee Clarence Thomas.
Ford would be called on to "fill in her story", Hatch said.
He did not comment directly on Ms Ford's claim that a drunken Kavanaugh and one of his friends trapped her in a room and attempted to pull her clothes off at a high school party in 1982.
Meanwhile, President Donald Trump, said today he wants "to hear what she has to say", "feels awful for...the unfair process" Kavanaugh has been subjected to.
"There's an agreement between the Federal Bureau of Investigation and the Senate Judiciary Committee, and whenever the Chair, speaking for the majority, wants a nominee investigated or re investigated, the FBI will do it", he said.
But top Republicans, including some who have expressed concern about Kavanaugh in light of the allegations, are indicating that they plan to vote on President Donald Trump's second nominee to the nation's high court if Ford doesn't appear before the panel on Monday. Dianne Feinstein (D-Calif.) have demanded that the hearing be postponed until an FBI investigation can be completed, the Department of Justice has stated that the FBI does not have jurisdiction in this matter.
Carlson said he was told by a senior USA official that the FBI will not investigate because what Ford is alleging is not a federal crime.
A source close to the president's son said Wednesday that he did not create the image, and that he wasn't mocking Christine Blasey Ford, the accuser who has turned Washington inside out in the past week. "And we want to get it over with", Trump said.
What are Trump and other Republicans saying?
While most Republicans have expressed support for Mr Kavanaugh, they have largely been careful to not criticise Professor Blasey Ford's assertions about what she says happened. He said it was "very hard" for him to imagine that Kavanaugh had acted as Ford has described.
He called the allegation against Judge Kavanaugh "a drive-by shooting".
"I'll listen to the lady, but we're going to bring this to a close", said the SC senator.
On Fox Business Network, Judge Andrew Napolitano was on with Neil Cavuto this afternoon discussing the nomination vote for Brett Kavanaugh in light of Christine Blasey Ford's accusation.
Fellow Republican Susan Collins of ME said on Wednesday that she hopes Prof Ford "will reconsider and testify" on Monday.
While Sen. Jeff Flake (R-Ariz.) had originally said that the hearing needed to be postponed until Ford's testimony could be heard, on Tuesday he said that if Ford refused to testify on Monday, the Senate should move forward with their vote.
The seat is opening up with the retirement of Republican Sen.