The International Building Code has new minimums on fireplace clearance:........ We found part of it was attached to the back of the fireplace with a wire mesh. I'm not sure if I can just drywall over this or not.
There are also Exceptions listed that may make your existing configuration OK. It's best to get a licensed fireplace contractor to look at it for an OK before any drywall work,from:http://www.rumford.com/code/IBC06.html
2111.11 Fireplace clearance. Any portion of a masonry fireplace located in the interior of a building or within the esterior walls of a building shall have a clearance to combustibles of not less than 2 inches (51 mm) from the front faces and sides of masonry fireplaces and not less than 4 inches (102 mm) from the back faces of masonry fireplaces. The air space shall not be filled, except to provide fire blocking in accordance with Section R1003.13.