The issue has arisen as the heir apparent, Princess Amalia, will turn 18 in December.
The Dutch monarch can marry someone of the same sex without giving up the throne, the Prime Minister has said.
In a written answer to questions from parliamentarians, Prime Minister Mark Rutte wrote on Tuesday that "the Cabinet does not see that an heir or the King would have to abdicate the throne if he/she wished to marry a person of the same sex."
Dutch royal weddings need the approval of parliament.
The questions arose following the publication of a book over the summer on the heir to the throne, "Amalia, Duty Calls".
Princess Amalia is the eldest child of King Willem-Alexander and will turn 18 on December 7. She graduated high school in June and announced she plans to take a gap year before attending university.
She has also turned down the €1.6 million annual allowance she was entitled to upon reaching 18, stating in a letter to Rutte earlier this year that she finds it "uncomfortable (to receive the money) as long as I do not do anything for it in return, and while other students have a much tougher time of it, particularly in this period of coronavirus."
In his letter to parliamentarians, Rutte did not answer definitively on the question of succession in the case of a same-sex marriage on whether a child born following a sperm donation or via a surrogate mother can be named "legitimate heir."
"Modern family law offers much scope for civil life to establish or have established family law relationships," Rutte wrote.
"There is a fundamental tension with the closed system of succession in the Constitution, which aims precisely to establish on objective and unambiguous grounds who will inherit the kingship.
It is not appropriate to anticipate now such a consideration of the succession," he went on, adding: "This depends too much on the facts and circumstances of the specific case, which, as can be seen with hindsight in the case of the family law, are not the same as in the case of the succession."