Well, to be technical the US does have colonies and territories--the largest of which is Puerto Rico, whose residents have no vote in US elections. There are a number of other small colonies with varying degrees of independence and representation (Guam, American Samoa, and the Virgin Islands).
And of course the US almost in it's entirety owes its size and natural resources to very real "empire building" in the 19th and 20th centuries.
Admittedly the territorial expansion of the US has slowed/stopped in the past 100-200 years, but it's not hard to understand how for someone belonging to a group that lived in a given place for many, many multiples of that duration, the current situation might feel, even today, like occupation. (see: hawaii sovereignty movement, native american reservations)
I suppose the question is "when does an empire stop being an empire?" Is it the day it stops expanding? 100 years later? When nobody remembers how things were "before"? I think it's an interesting question.
(1) : a major political unit having a territory of great extent or a number of territories or peoples under a single sovereign authority; especially : one having an emperor as chief of state
(2) : the territory of such a political unit
b : something resembling a political empire; especially : an extensive territory or enterprise under single domination or control
2 : imperial sovereignty, rule, or dominion
3 capitalized
[Empire State, nickname for New York]
: a juicy apple with dark red skin that is a cross between a McIntosh apple and a Red Delicious apple
Since the US does not have a single authority controlling it (i.e. "is a democracy") it cannot be an empire. They are mutually exclusive according to the dictionary.
Being a democracy or not doesn't really have anything to do with being an empire, generally you have an empire when you have a state substantially composed of multiple nations. But generally with imperial democracies its only one nation that is a democracy, like in the British Empire where Britain, a democracy, ruled a huge colonial empire.
If you really squint hard you could argue that the rest of NATO are military tribute states giving soldiers to the US empire but that's a very strained interpretation. Japan is currently pretty dependent on US military protection but that doesn't seem to have turned into economic exploitation. Certainly American efforts to get Japan to open up to more US exports isn't something Japan has just rolled over on.
But the current international system does have the US at its center and colloquially people call this the American Empire, and we know what they're talking about even if it isn't really an empire.
Democracy and empire are not mutually exclusive. Not that the US is a democracy, exactly, but regardless, Athens, Rome, Britain, were all flavors of democratic when they expanded into imperial activity.