In the first season (The goddess goes to the Dragon King Palace) Nanami asks Isohime to remove the eye from her. But in the same episode, it is shown that the eye was consumed by Yukiji in the past.
So how did the eye go from Yukiji to Nanami?
In the first season (The goddess goes to the Dragon King Palace) Nanami asks Isohime to remove the eye from her. But in the same episode, it is shown that the eye was consumed by Yukiji in the past.
So how did the eye go from Yukiji to Nanami?
Spoilers ahead...
TL;DR: Nanami is a direct descendant of Yukiji. So the eye mystically passed from parent to child until it ended up inside Nanami.
After a girl of Yukiji's lineage gets pregnant (and they can only have girls) The eye passes on to the child, leaving the mother's system. Since Yukiji's bloodline is very weak, this means the mother dies soon after childbirth, but the child becomes quite healthy due to the eye's properties.
There is a deeper backstory in the Manga, and I will quit here in order to spoil the least possible.
Perhaps Yukiji is Nanami's ancestor so maybe the Dragon King's Eye went through her when she was born.