The Shukan Bunshun quoted an unidentified friend who said the prince told him the tightly guarded news three months ago.
"A close friend asked Prince Akishino, 'After having two daughters, Princesses Mako and Kako, would the next baby be a boy?'" the weekly said.
"Prince Akishino smiled and clearly responded: 'Yes, it seems that way'," the magazine said.
The 39-year-old Princess Kiko is expected to give birth by Caesarean section next week.
Japan has been holding its breath for months, with much of the public holding high hopes for a boy to maintain the male-only succession of the world's oldest monarchy.
The palace is yet to announce the gender of the fetus, only saying it is developing healthily.
If the baby is a boy, it would be the first male born to the imperial family since Akishino himself in 1965.
Crown Prince Naruhito and Crown Princess Masako have one child, four-year-old Princess Aiko.
Masako, a US-educated former career diplomat, has suffered years of stress due to pressure to bear a boy and adapt to the tradition-bound monarchy.
The crown couple and their daughter returned Thursday from a two-week holiday in the Netherlands, the first time a Japanese royal has gone overseas for recuperation.
Japanese media broadcast rare footage of a beaming Masako and Aiko during the vacation, in contrast to the mother and daughter's usual formality in Japan.
Kiko's pregnancy was a dream come true for conservatives as it led Prime Minister Junichiro Koizumi to backtrack on widely supported reforms to allow a woman to ascend the Chrysanthemum Throne.
Chief Cabinet Secretary Shinzo Abe, a conservative who is the front-runner to succeed Koizumi in late September, expressed his caution Thursday about sudden changes to succession rules.
"Royal succession affects the base of our nation, and it is extremely important that we create a system that ensures stable succession," Abe, who has said little recently on the succession debate, told reporters.
"The government wants to work carefully and calmly so that we can gain consensus from all parts of the public," he said, adding that he was praying for Kiko's safe delivery.
The Shukan Bunshan said ruling party lawmakers, medical experts and journalists who cover palace affairs already talk as if the baby will be a boy.
The friend of Akishino told the magazine, however, that there is still a room for uncertainty.
"The comment was said at a time when it was possible to tell the sex of the baby, but he is not the type of person who would casually disclose such an important piece of information," the friend told Shukan Bunshun.
The magazine said it was possible that Akishino was not confirming the sex of his long-awaited baby but instead was trying to avoid disappointing his friend who hoped for a boy.