Major developments in the lawsuit are expected during a hearing on Tuesday, just one day after the 2009 settlement agreement between Epstein and Ms Giuffre is made public.
The Guardian reports that Ms Giuffre's legal team is claiming that they have found up to six witnesses who can link Prince Andrew to Ms Giuffre.
Prince Andrew has repeatedly denied any wrongdoing. He claims he was at a Pizza Express in Woking on the night Ms Giuffre claims the pair had sex, and has been challenged to name any witnesses to support his alibi.
The prince is a former friend of Ghislaine Maxwell, who was last week convicted on sex trafficking charges tied to her time working with Epstein.
On Thursday Maxwell was found guilty on five of six counts against her, including sex trafficking a minor. She is believed to have operated as a pimp and recruiter for Epstein.
Prince Andrew was not named in Maxwell's trial, and her conviction does not have any legal implications for the lawsuit involving the prince.
Ms Giuffre, however, may be called to give a victim impact statement at Maxwell's sentencing hearing.
The next major action in Ms Giuffre's lawsuit will take place on Tuesday, when Judge Kaplan decides if her civil claim against Prince Andrew can proceed to trial.