Initially, Hillary Clinton, 78, is expected to testify under oath on Thursday before her husband and former president Bill Clinton, 79, is questioned on Friday.
According to US media, they will be questioned not in Congress in Washington, but via video link.
These are expected to be closed sessions so it is unclear how much information will be made public.
Hillary and Bill Clinton refused for months to testify before the US Congress in the investigation of the Epstein case.
The Democrats accused the Republican chairman of the relevant House oversight committee, James Comer, of conducting a politically motivated investigation.
According to US media reports, their agreement to testify in early February led to the Republicans cancelling a vote on a contempt of Congress procedure against the Clintons.
Bill Clinton's name and pictures of him appear in documents related to the Epstein investigations.
However, a mention in itself means nothing.
The former president has repeatedly denied any wrongdoing in connection with his acquaintance with Epstein.
Epstein operated an abuse ring for years, victimising dozens of young women and minors.
The New York financier had excellent connections in US high society.
He died in his prison cell in 2019 before a conviction could have been reached.
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