This new investigation was launched last week on President Donald Trump's orders, in relation to claims from Dr. Christine Blasey Ford, who says Kavanaugh sexually assaulted her when they were in high school.
The controversy over Kavanaugh's nomination - which could be put to a final vote in the Senate as early as Saturday - comes ahead of November congressional elections in which Trump's Republican Party will battle to keep control of Congress. A handful of Republican and Democratic senators are undecided on whether to support Kavanaugh and their votes will decide whether he is confirmed.
Besides Flake and Collins, Republican Lisa Murkowski of Alaska and Democrats Joe Manchin of West Virginia and Heidi Heitkamp of North Dakota have yet to declare their positions on Kavanaugh.
Ms Collins, a moderate Republican from ME, told reporters on Wednesday: "The president's comments were just plain wrong".
Federal Bureau of Investigation agents interviewed three people in connection with the allegations made by Christine Blasey Ford, who says that Kavanaugh sexually assaulted her in high school.
Kavanaugh also testified before the committee - and vehemently denied the allegation.
Ford's lawyers said it is "inconceivable" that the FBI could conclude its investigation, which could happen as early as Wednesday, without interviewing either her, Kavanaugh or all of the other witnesses whose names she has provided.
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Its nine justices are appointed for life and have the final say on some of the most contentious issues in USA public life, from abortion, to gun control, to voting laws. But it raises questions about how such words will affect five senators - all moderates - whose votes on Kavanaugh will be decisive.
Kavanaugh has denied the accusations by all three women.
White House spokeswoman Sarah Sanders also defended Mr Trump, telling a press briefing that the President was not concerned the comments may have endangered the votes of key senators.
In a statement, White House spokesman Raj Shah said: "With Leader McConnell's cloture filing, Senators have been given ample time to review this seventh background investigation".
Kavanaugh's truthfulness to Congress - including how he represented his alcohol consumption - is also under the scanner, with a former Yale classmate on Monday accusing the judge of misleading lawmakers when he said he never experienced blackouts. According to Kavanaugh's 1982 calendar, he hosted a party that included several people that Ford identified as being present on the night she was assaulted.
The newspaper cites sources close to the investigation who say the Trump Administration is preparing to send the FBI's final report to a Senate Judiciary Committee today. For example, Republicans will spend an hour with the report from 8 a.m. until 9 a.m. Thursday, then Democrats will have an hour with the report. Lawyers for Ford, who alleged that Kavanaugh sexually assaulted her more than three decades ago, complained in a letter to Wray this week that they had gotten "no response" when they requested that agents interview their client. Even President Trump, after days of calling Ford "credible", changed his tune and mocked Ford at her during a rally in Mississippi Tuesday night, a day after the poll was conducted.
Imitating Ford, he added, "But I had one beer - that's the only thing I remember". 'I don't know.' Upstairs, downstairs, where was it?
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".