The 2016 deposition is scheduled for release on Aug. 3, unless the appeals court orders a delay or further arguments.
If the documents are released, they are likely to shed more light on Maxwell's dealings with Epstein, as well as Epstein's own conduct.
Maxwell, 58, has denied charges she lured underage girls for Epstein to sexually abuse and has pleaded not guilty.
Dershowitz and Barak are allegedly among the men, to whom Giuffre was trafficked.
The judge scheduled a trial date for July 12, 2021.
She also said she is not a flight risk, citing her lack of a prior criminal record and her having remained in the United States after Epstein's arrest last July.
Prosecutors said Maxwell groomed girls so Epstein abuse them at lavish homes in Palm Beach, Florida; New Mexico and Manhattan.
Maxwell is likely in her own holding cell where she can be observed at all times, said Ted Lothstein, another New Hampshire criminal defense lawyer.