A judge said he will decide on Friday whether Timothy McVeigh's execution can be broadcast on the internet.
The Entertainment Network Inc said Americans have a constitutional right to see the execution.
The Justice Department disagrees.
Judge John Tinder, of Indiana's Southern District court will announce his decision on the lawsuit on Friday.
Entertainment Network chief executive David Marshlack said: "This is something that is our constitutional right. We're paying for it, it's our tax dollars paying for it. This event is large, it's touched so many people's lives.
"We should be able to view it if we want to. We should be able to put closure to it."
The Newsbytes website quotes Justice department spokesman Chris Watney as saying: "The media does not have a constitutional right to visually record and broadcast the execution of a condemned criminal."
McVeigh has asked for his execution to be broadcast live on national TV but federal prison regulations ban public broadcasts of executions.
He is due to be executed by lethal injection on May 16. Families of his victims will be allowed to watch him die by CCTV.