Clinton, the 2016 Democratic presidential nominee, has said she has little information to provide and has accused the Republican-led panel of trying to shift focus away from President Donald Trump's ties to Epstein, who died by suicide in jail in 2019 while awaiting trial on federal sex-trafficking charges.
She and her husband, Democratic former president Bill Clinton, initially refused to testify before the House of Representatives oversight committee, but relented when lawmakers moved to hold them in contempt of Congress.
Hillary Clinton is due to deliver a closed-door deposition to the committee in Chappaqua, New York, near their main residence.
Bill Clinton is scheduled to testify on Friday.
A spokesperson for the Clintons did not respond to a request for comment.
Committee chairman James Comer, a Republican, has said transcripts of their interviews will be made public.
Hillary Clinton's ties to Epstein are unclear.
Bill Clinton flew on Epstein's plane several times in the early 2000s after he left office.
He has denied wrongdoing and expressed regret for his association.
According to Comer, Epstein visited the White House 17 times while Clinton was in office.
Trump also socialised extensively with Epstein in the 1990s and 2000s, before his 2008 conviction for soliciting prostitution from a minor.
Comer said evidence gathered by the panel does not implicate Trump.
Trump's Justice Department has released more than three million pages of Epstein-related documents over the past several months to comply with a law passed by Congress.
The Justice Department sought to draw attention to photos of Bill Clinton, but the documents also have revealed Epstein's ties to a long list of business and political leaders, including Commerce Secretary Howard Lutnick and Tesla CEO Elon Musk.
Overseas, they have prompted criminal investigations of Britain's Andrew Mountbatten-Windsor, the former duke of York, and other prominent figures.
