The government is in the final stage of formalising the schedule, said the Asahi, citing several sources.
Ahikito, 83, who has had heart surgery and treatment for prostate cancer, said in rare public remarks last year he feared age might make it hard for him to continue to fulfil his duties.
He will be succeeded by Naruhito, 57, and a new era will start from April 1, the Asahi reported.
The expected schedule would minimise the impact on people in changing to a new imperial reign from the current Heisei Era, which started in 1989 after the death of Akihito's father Hirohito, according to the Asahi.
Also, the Imperial Household Agency wanted the transition to take place in spring 2019 as many ritual events are scheduled for the imperial family in autumn and winter, the report said.
Akihito, the first Japanese emperor who was never considered divine, has worked for decades at home and abroad to soothe the wounds of World War Two which was fought in his father Hirohito's name.
In a written remarks of her 83rd birthday on Friday, Empress Michiko said that she thought this year her travels with Emperor Ahikito around Japan might be their last and have become deeply emotional.
The Empress also said she felt "an immeasurable sense of peace" that Akihito will be able to rest and spend quiet days after years of pursuing how the Emperor should be.
(Reporting by Kaori Kaneko; Editing by Michael Perry)
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