In the most common use of the term, you would not say "there is none." "None" is normally used in a context where there is a potential for there to be several of the object, but there aren't any.

however, you talk about an object that can be divided in the singular using the word. For example, "Is there any pie left? No, there is none left," or "that is none of your business" (it's unclear to me whether that's singular or plural.) Or you could say, "I'll have none of that!" when expressing your desire to have nothing to do with or no part in something, and that can be sort of singular, like "that corruption," "that conspiracy," etc.

The obvious, cheater exception would be a reference to the word itself. Like, "that 'none' doesn't belong in this sentence."

hope that helps!