In a federal court suit, Abdul Awkal contends Jewish inmates get kosher food, but his non-halal meals impinge his religious freedoms.
Ohio officials said they recently removed pork from its menus, but providing halal meals would strain its already-tight budget.
A second non-death row inmate has joined Awkal in his suit.
They say the vegetarian and non-pork options are not good enough and food must be prepared in compliance with Islamic law, which requires an animal's throat to be slit to drain its blood.
"The issue of eating halal meals is especially important to me because I face a death sentence," Awkal said in court papers.
Lawyers for both sides have until next month to file their arguments. The case is expected to go to trial in January.
Awkal, 52, is on death row for killing his estranged wife and brother-in-law in a room in Cuyahoga County Domestic Relations Court, in Cleveland, in 1992.
He is scheduled to be put to death in June.
