There was no immediate confirmation of the reports by Jiji Press and other media, but a Justice Ministry spokesman said a press conference on the issue was being prepared.
Japan and the United States are the only major advanced industrial nations with capital punishment.
Surveys have shown that the death penalty has overwhelming public support in Japan, despite repeated protests from European governments and human rights groups.
International advocacy groups say Japan's system is cruel because inmates can wait for their executions for many years in solitary confinement and are only told of their impending death a few hours ahead of time.
Japan in 2009 launched a jury system in which citizens deliberate with professional judges in a bid to boost the role of the citizenry in the judicial process.
Under the system, more than a score of people have been sentenced to death, according to public broadcaster NHK.