The base technology required to make dried and/or smoked sausages, as a means to preserve meat and stuffing it in intestines for easy transportation, is very simple, and would have been available to every prehistoric hunter/gatherer society.

It is also something that does not leave any tangible evidence behind for archaeologists to discover, so the specific geographical origins of the sausage are lost to us, but it would be reasonable to suggest that it would be in the general area where humans first discovered and applied fire and stone cutting tools.