Virginia Giuffre is seeking damages after alleging that the Duke of York sexually assaulted her when she was under 18. He vehemently denies the allegations.
They are part of a civil claim which is being brought through the US courts.
If the case progresses to the discovery pre-trial stage, Andrew’s family members and aides could have to testify.
During his BBC Newsnight interview, the Duke claimed that on the night Ms Giuffre alleged they were in London he had taken his daughter to Pizza Express in Woking while Sarah was away.
Courtiers fear the Duchess is likely to be subpoenaed as her whereabouts is part of Andrew’s alibi, the Sunday Telegraph reported.
Bradley Simon, a former federal prosecutor in New York who now works as a defence attorney specialising in complex civil litigation, told the newspaper: “They’re going to ask for a kitchen sink.
“They’re going to seek every correspondence, phone logs, emails, diaries.
“They’re going to go after people who were with him. It’s going to be open season.”
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The Duke has denied all the allegations.
Andrew’s legal team is attempting to get the case thrown out.
In a previous legal hearing the Duke’s Los Angeles-based lawyer Andrew Brettler said that Ms Giuffre had previously entered into a “settlement agreement” with Epstein in 2009 that would nullify her case.
It was confirmed that the Duke officially received court papers relating to a sexual assault lawsuit on September 21.
The issue of whether or not Andrew had been notified about the case – known as service of proceedings – was contested during the first pre-trial hearing of the civil case in New York.
The Duke has until October 29 to provide a response.