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WASHINGTON, DC - OCTOBER 04:  Comedian Amy Schumer waits to be led away after being arrested during a protest against the confirmation of Supreme Court nominee Judge Brett Kavanaugh October 4, 2018 at the Hart Senate Office Building on Capitol Hill in Washington, DC. Senators had an opportunity to review a new FBI background investigation into accusations of sexual assault against Kavanaugh and Republican leaders are moving to have a vote on his confirmation this weekend. (Photo by Alex Wong/Getty Images)
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WASHINGTON, DC - OCTOBER 04: Comedian Amy Schumer waits to be led away after being arrested during a protest against the confirmation of Supreme Court nominee Judge Brett Kavanaugh October 4, 2018 at the Hart Senate Office Building on Capitol Hill in Washington, DC. Senators had an opportunity to review a new FBI background investigation into accusations of sexual assault against Kavanaugh and Republican leaders are moving to have a vote on his confirmation this weekend. (Photo by Alex Wong/Getty Images)
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(CNN) —  

Whether the FBI interviews Brett Kavanaugh and Christine Blasey Ford, the woman accusing President Donald Trump’s Supreme Court nominee of sexual assault, is up to three key undecided Republican senators, according to people briefed on the FBI’s background investigation.

Ford and Kavanaugh weren’t on the initial list the White House provided for the FBI to interview, and the sources tell CNN they still aren’t.

The White House counsel’s office, which is coordinating the FBI, believes the sworn testimony from the two is enough and there’s no need for an FBI interview. This despite the fact that the interview list has grown to include other possible witnesses, CNN has reported based on attorneys for people who have been contacted.

While the key senators – which includes Susan Collins of Maine, Lisa Murkowski of Alaska and Jeff Flake of Arizona – aren’t dictating the terms of the investigation (that responsibility resides with the White House), their role as undecided votes who will determine whether Kavanaugh is the next Supreme Court justice has been crucial, senators and aides say. The three were responsible for pushing Majority Leader Mitch McConnell and Senate Judiciary Committee Chairman Chuck Grassley to ask the White House for the inquiry to begin with – a move McConnell made clear he opposed.

And their efforts to ensure the FBI hasn’t been unnecessarily hemmed in as they do their work continued through last weekend.

The senators have been in consultation with the White House about the scope of the investigation and were instrumental in the decision on the original list of four individuals the FBI would interview – a list that didn’t include Ford or Kavanaugh. Since then, all have made clear that the FBI should be free to follow any new leads, but to this point haven’t asked the FBI to sit down with Ford or Kavanaugh.

Flake told CNN’s Manu Raju that Ford “gave testimony before the committee,” and that he is “more concerned about corroboration and people,” than an FBI interview with Ford. Flake said the FBI should follow “leads that she had mentioned, people that she had talked to, particularly Mark Judge and others that she places in the room. That is where they needed to start and then follow those leads wherever they go.”

With the White House’s blessing, the FBI has expanded its inquiry into allegations against Kavanaugh beyond the initial four interviews that the White House directed to be conducted, and have now also spoken with more of Kavanaugh’s classmates from Georgetown Prep who attended a party entered onto Kavanaugh’s 1982 calendar.

Ford’s lawyers have demanded the FBI interview her, and in a letter yesterday to the FBI said, “It is inconceivable that the FBI could conduct a thorough investigation of Dr. Ford’s allegations without interviewing her, Judge Kavanaugh, or the witnesses we have identified in our letters to you.”

The FBI has been working very closely with the White House and has been keeping White House counsel Don McGahn updated on its work. The details of the first interviews were shared with the White House and that is how some of the additional interviews then came about.

One of those interviewed by the FBI is Deborah Ramirez who alleges that Kavanaugh exposed himself to her and others in a dorm room when they were Yale freshmen. Kavanaugh has denied Ramirez’s allegations. Ramirez’s lawyers have provided the FBI with the names of more than 20 individuals who they say can help corroborate Ramirez’s story. Only a small number of those, however, may have witnessed the alleged incident. It is those individuals to whom the FBI may also be talking. Those interviews would require the White House’s approval.

The FBI is still constrained by the parameters set by the White House, which is a very limited supplemental background investigation – not a criminal investigation.

A source familiar with the work so far says the FBI is currently in information collection mode. Just because they haven’t spoken with Ford doesn’t mean they won’t eventually want to do so after all key info is collected — it’s not unusual to wait to interview a key witness after other witnesses have been interviewed — that said it will ultimately be up to the White House to greenlight a Ford interview.

The FBI could complete its interviews Wednesday and provide investigative summaries to the White House and Senators soon after.

CNN’s Josh Campbell, Manu Raju and Shimon Prokupecz contributed to this report.