The 82-year-old monarch has told those close to him that the role should be occupied by someone who can fulfil the emperor's duties as stipulated in the constitution, public broadcaster NHK reported, without citing a source for the information.
Under Japan's current Imperial Household Law, which governs the status of the emperor, there is no legal mechanism for abdication.
Any move to step down would therefore require a revision of that law.
Kyodo News agency carried a similar report, citing an unnamed government source.
More From This Section
Crown Prince Naruhito and the emperor's wife, Empress Michiko, support the wish, NHK said.
Japan, which claims to have one of the world's oldest monarchies, has not seen an imperial abdication from the Chrysanthemum Throne in 200 years, NHK said.
Akihito's role is strictly limited to one of "symbol of the state" under a constitution imposed by the United States in the aftermath of World War II.
His father Hirohito, in whose name the military conquests of the 20th century were prosecuted, was treated as a living god in Japan until defeat in 1945.