Trump ordered the agency to reopen the background check into Supreme Court nominee Brett Kavanaugh with the stipulation that it be completed within a week after the Senate Judiciary Committee requested the president make the request for a "supplemental" investigation.
Besides Ford, two other women have made similar allegations of misconduct.
In a tweet on Sunday, Times reporter Sheryl Gay Stolberg quoted Ford's lawyer, Debra Katz, as saying: "We have not heard from the Federal Bureau of Investigation, despite repeated efforts to speak with them".
White House counsellor Kellyanne Conway delivered a similar message Sunday, repeating that the investigation will be "limited in scope" and "will not be a fishing expedition".
The president revisited the question of the scope of the FBI's probe in a late- night tweet on Saturday, writing in part, "I want them to interview whoever they deem appropriate, at their discretion".
Kavanaugh on Friday continued to defend himself and said he will be cooperating with FBI investigators.
Swetnick is represented by the attorney Michael Avenatti, who tweeted on Saturday that the White House's restrictions would "undermine the legitimacy" of the entire investigation. Following the agreement for the FBI to investigate Kavanaugh, the focus has moved to how the probe will be handled, its ultimate findings and whether it will put to rest fears about a lack of due diligence over the nominee for the nation's highest court. Is that because she is not on the White House-approved witness list?
But Tobias said FBI agents were usually allowed to act independently and it would be a "clear conflict of interest" for White House officials involved in Kavanaugh's confirmation process to interfere with the FBI's investigation.
One of the key swing votes in the confirmation of Brett Kavanaugh to the U.S. Supreme Court said Sunday the judge's emotional denial of sexual misconduct convincingly sounded like someone who had been "unjustly accused".
"I wonder - could you have done this if you were running for re-election?"
Comey also alluded to the apparent discrepancy between statements Kavanaugh made to the committee about his drinking habits in high school and college, and what some of his former classmates remember based on their encounters with him.
Democratic Sen. Chris Coons said he thought some of Kavanaugh's exchanges with Sens. She did not identify Kavanaugh or Judge as one of her attackers.
Sanders said Trump, who has vigorously defended Kavanaugh but also raised the slight possibility of withdrawing the nomination should damaging information be found, "will listen to the facts".
White House spokesman Raj Shah said the Senate set the scope and duration of the investigation and that the White House is "letting the FBI agents do what they are trained to do".
Kavanaugh said in a statement that he had done "everything" requested of him and would "continue to co-operate".
Ford testified Thursday before the Senate Judiciary Committee that Kavanaugh sexually assaulted her in high school.
Republicans control 51 seats in the closely divided 100-member Senate and can not afford to lose more than one vote on confirmation.
Flake told Pelley he had to hit the "pause button" after being confronted in an elevator on Friday morning.
Judge's lawyer, Barbara Van Gelder, said in a statement that Judge "vehemently denies the allegations contained in the Swetnick affidavit".
But she then added that it was unfair to condemn Kavanaugh for an alleged action 36 years ago that could not be confirmed.