Well, that's an interesting question. I have several theories on their possible existence.
If they currently exist, they could be microscopic bacteria floating around in our solar system. The word "alien" means foreign or from another world, so any living thing that isn't on Earth would an alien. Therefore I believe if any bacteria can survive in the atmospheric conditions of space, they would be considered an alien, at least to my perspective.
Another theory is that, who knows, what if humans turn into aliens into the future? We're the most intelligent species on the planet, exploring outer space, mostly hairless, and have already made major advancements in technology over short periods of time. Perhaps thousands of years later some humans that descended from space explorers would be the aliens, and maybe speak a different language for all we know.