The idea is being floated as a way to limit the impact of changing era names on people's lives by applying the new one at the start of 2019, according to the source.
The government is in the process of exploring an early succession by the 56-year-old crown prince in light of the emperor's advanced age, the source said.
The 83-year-old emperor strongly hinted at his desire to abdicate in a rare video message in August.
Members of the government took 2018 as the time limit as Emperor Akihito stated in the message, "A major milestone year marking the 70th anniversary of the end of World War II has passed, and in two years we will be welcoming the 30th year of Heisei." The 30th year of Heisei falls in 2018.
Prime Minister Shinzo Abe's government plans to submit to the next ordinary Diet session, to be convened later this month, a bill for special legislation that would enable the emperor to abdicate and apply only to him.
Although the first day of 2018 could provide a suitable milestone, if the legislation is enacted as planned, it would be too soon for sufficient preparation, the source said.
As to the timing of the current emperor's retirement, one idea is to include it in the special legislation while another is to stipulate in an ordinance, the source said.
Chief Cabinet Secretary Yoshihide Suga has declined to clarify the timing, telling a regular press conference Tuesday that a government-commissioned panel is continuing its discussions, focusing on how to alleviate the burden on the emperor.
The six-member panel is expected to release a report summarizing issues pertaining to the emperor's possible abdication as early as Jan 23.
Before that, the heads and deputy heads of the Diet's two chambers will hold a meeting Jan 16 to discuss how the legislative body should handle the special legislation, the chairman of the House of Representatives steering committee said Tuesday.