There doesn't seem to be much mention about how to create / hatch a Basilisk except for:
Of the many fearsome beasts and monsters that roam our land, there is none more curious or more deadly than the Basilisk, known also as the King of Serpents. This snake, which may reach gigantic size, and live many hundreds of years, is born from a chicken's egg, hatched beneath a toad. Its methods of killing are most wondrous, for aside from its deadly and venomous fangs, the Basilisk has a murderous stare, and all who are fixed with the beam of its eye shall suffer instant death. Spiders flee before the Basilisk, for it is their mortal enemy, and the Basilisk flees only from the crowing of the rooster, which is fatal to it."
Harry Potter and the Chamber of Secrets
Is there any references to if the breeder has to be a wizard, or can muggles or non-human magical beings do so as well?