Several townships require fireproofing around furnaces. The requirements vary from township to township. The local fire marshal or building inspector should be able to tell you what is required and what materials are acceptable.
Around here, some townships require a fire resistant vault be constructed around the furnace. I have had to install several. They usually consist of a fire resistant closet with a fire rated door. Often 2 layers of drywall with fire rated caulking will suffice for the closet construction, others may require something more substantial like cinderblock. Also, unless your furnace has its own outside air supply line leading to it, be sure you have the proper vents into the closet.
Maybe all you need is drywall on the ceiling above the furnace?.....so, check with your township.