WAVY-TV of Portsmouth, Virginia, one of the media entities involved in the court action, said the hearing is set for 10 a.m. EDT (1400 GMT). Joining the media organizations will be Pasquotank County Sheriff Tommy Wooten, the station reported.
Brown, a Black man, was fatally shot by deputies of Wooten's office last Wednesday. Wooten has said the officers were attempting to serve search and arrest warrants on Brown related to felony drug charges.
Lawyers for the Brown family have accused the officers of "executing" the 42-year-old. On Tuesday, they said an independent autopsy showed he died from a "kill shot" to the back of his head.
Also on Tuesday the FBI said it had opened a civil rights investigation of the shooting.
The shooting has led to a week of protests in Elizabeth City, a riverfront community near the Virginia border. The shooting happened one day after former Minneapolis police officer Derek Chauvin was convicted of murdering George Floyd in a trial that put a spotlight on police violence against Black people.