As part of the case she will have to testify under oath, but she wants that testimony off limits to the public.
If it's made public she says it would be an "invasion of privacy."
Earlier this week, Young filed a motion to dismiss the case, because Hunter has not shown up for a deposition.
The court document states a deposition was scheduled for Wednesday, but Hunter backed out for a second time.
The motion pointed out Hunter would not agree to answer questions under oath unless the transcript was sealed.
Young's motion points out Hunter answered personal questions for "GQ Magazine" and posed for pictures "partially undressed."
The existence of the sex tape came to light after Young's book "The Politician," hit the stands in February. In the book, Young documents his years working for Edwards and talks about his role hiding the existence of Edwards' affair with Hunter from the media while he ran for president.
Hunter sued the Youngs for invasion of privacy and demanded the tape back. The Youngs were ordered to turn over all copies of the tape and other material to the court while it determines ownership.
Young admitted there are some missing items he can't account for, but says he has given the court everything it has requested.
Last month, attorneys for Hunter said the Youngs have held back copies of the tape.
The Young's lawyers have argued that she gave up ownership of it by abandoning it and not trying to claim it for several years.