import bpy

#example path to store files
path = '/Users/Steve/Desktop/'

#store selection
obs = bpy.context.selected_objects
    
for ob in obs:
    #deselect all but just one object and make it active
    bpy.ops.object.select_all(action='DESELECT')
    ob.select_set(state=True)
    bpy.context.view_layer.objects.active = ob
    
    #store object location then zero it out
    location = ob.location.copy()
    bpy.ops.object.location_clear()
    
    #export fbx
    filename = path + ob.name + '.fbx'
    bpy.ops.export_scene.fbx(filepath=filename, use_selection=True)
    
    #restore location
    ob.location = location
  
#reselect originally selected objects  
for ob in obs:
    ob.select_set(state=True)