The Imperial Household Agency declined to confirm the report today.
Kei Komuro, the man who won the princess' heart, was a fellow student at International Christian University in Tokyo, where Kako, 25, also graduated, NHK said.
They met at a restaurant in Tokyo's Shibuya about five years ago at a party to talk about studying abroad, and they have been dating several times a month recently, it said.
Women can't succeed to the Chrysanthemum Throne in Japan. Kako's father and her younger brother are in line to succeed Emperor Akihito, but after her uncle Crown Prince Naruhito, who is first in line.