I think Godzilla is either genderfluid or an asexual female. Either way he's asexual. In some iterations, like Godzilla 1998, he doesn't have any... uh... you know what I mean. However, he is still shown feeling attraction to other kaiju, like Komodithrax. He raises her egg before her tragic death along with the egg. But maybe he's like a jellyfish and has both the ability to give and receive sperm. I don't know man I was bored. I think it's open to interpretation though.
Toho. Me.