In the advent prologue David refers to the alien as the wolf. Which does makes sense with the satanic mural of the Alien in Prometheus. Even if that creature was meant to be the Deacon, it still looks far too alien. Also the creature in the mural next to the engineer looks similar yet different to the alien as well. However each host dna produces a unique form of the alien. So I think it is reasonable to concluded that the deacon/mural/alien are all cousins to one another.
Although when thinking about how close the alien of Covenant is to the Alien, I suppose the only step left is to impregnate an engineer to get it's biomechanical parts.