At issue are concerns about protecting the girl and worries raised by an attorney for defendant Ma'Lik Richmond that keeping the trial open could lead to potential witnesses on his behalf being intimidated.
News organizations including The Associated Press have argued that openness is the best way to ensure public confidence in the proceedings.
Judge Thomas Lipps, a special judge brought in from Hamilton County to oversee the trial, was set to hold a hearing Friday to take testimony from both sides, then decide. The judge has already rejected a request to try the two players separately.
The football players are accused of attacking the girl twice after an alcohol-fueled party in mid-August in Steubenville in far eastern Ohio. Three other students who witnessed the attack but weren't charged are expected to testify at next month's trial. The girl attends a different high school across the river in West Virginia.
The girl and her parents want the trial closed to keep evidence that a judge might rule inadmissible from becoming public, their attorney argued in a court filing Tuesday. That could include "harmful" and "legally non-relevant" evidence, said attorney Robert Fitzsimmons.
Keeping the hearing closed will also protect the girl, who has maintained her anonymity through the proceedings, Fitzsimmons said.
The AP generally doesn't identity people who say they are the victims of sexual assault.
Attorney General Mike DeWine, whose office is prosecuting the case, says it will be difficult enough for the girl to testify, let alone in a public hearing open to the media.
News organizations arguing to keep the hearing open say the case is already subject to speculation that it won't be fully investigated and prosecuted because it involves the city's popular football team. Keeping it open eliminates that speculation, according to arguments by the AP, ABC, CNN, CBS News, The New York Times and WEWS-TV.
The lawyer for Richmond wants the trial closed out of concern that intense publicity and social media commentary could lead to witness intimidation. The attorney, Walter Madison, cited threats he said were made by the hacker-activist group Anonymous to retaliate against people perceived as helping his client.
The other defendant has asked that the case be delayed and moved but not closed.