Well, to "start at the beginning" as far as speculative cosmology goes, I believe there are some notions implied by the term "extra terrestrial" which problematise its application to ancient conceptions of a universe containing a multiplicity of worlds. The conceptualisation of other worlds as physical bodies separated from earth by a common traversible medium which, however it might differ in construction, shares a plane of existence with and obeys physical laws in common with the earth itself simply isn't a construction of the cosmos the ancient world saw. So from the point of view of, say, Anaximander, while there might be many worlds, existing over immense time scales, the notion of beings existing on one world, in one time (and one might even say in one plane of existence) implicitly signifies nothing whatsoever for any other such world. The modern notion of "extra-terrestrials" implies the existence of beings from elsewhere than the earth which nonetheless share our universe, and might interact with us simply by travelling sufficiently far. It seems to me questionable whether something can be deemed an "extra-terrestrial" in the sense we usually mean, which in a very real sense exists outside our sphere of reality and causality.

It seems to me there are a couple key ingredients required, to allow for the modern idea of extra-terrestrials:

1. The heliocentric model, which, in combination with the proposition that the stars are themselves just distant suns (which had been offered, in the ancient world, in both China and Greece), promotes the notion that there are likewise a multiplicity of planets associated with these stars. If the sun is simply an exceptionally near star, in orbit around the earth, there is no reason to presume the existence of distant stars implies distant planets.
2. The notion of a constitution of the "heavens" which does not make them a discrete plane of reality or physicality from the terrestrial one. If the earth's surroundings, in the cosmos, are an essentially different sphere of existence, one is not inclined to assume that there might be planets simply floating around out there in a physical state similar to our own.

What would you define as "the modern concept"? Ideas of lifeforms on other planets are pretty darn old, and are actually less common nowadays than they were in the past.

So, perhaps if you are more specific about what you mean with "modern concept of aliens" I can look up in the literature when people started talking about aliens in that specific way :)