They aren't the betting favorite because, like the other contenders, there are flaws on their resumes, too.
The royal sported a flawless complexion with natural looking makeup and had her brunette locks pulled back.
The expert claimed the royal press office had been told to prepare for an announcement on the subject.
The princess is already a mum to Christian, 11, Isabella, 10, and six-year-old twins Vincent and Josephine.
Crown Prince Naruhito's visit to Denmark celebrated the 150th anniversary of diplomatic relations between Denmark and Japan.
For her boat trip with the prince, the mother-of-four looked ever-sophisticated, finishing off her look with diamond earrings and a golden necklace.