The test is scheduled for a stretch of ocean southwest of Tokyo, between Shizuoka and Wakayama prefectures, over several weeks in the fiscal year to March 2013, the Nikkei financial daily said.
The Ministry of Economy, Trade and Industry is preparing to request more than 10 billion yen ($127.5 million) for the project, the report said.
The government will support further research and aims for commercial drilling to start early in the next decade, the newspaper said.
Methane hydrates are found in environments with high pressure and low temperatures such as the ocean floors, often near continental faultlines, where the gas crystallises on contact with cold sea water.
The offshore experiment, if successful, would be the world's first, the Nikkei said. Methane was previously extracted from methane hydrate on land in Canada in 2008 using technology developed in Japan.
Japan has been looking to diversify its energy resources since the powerful March 11 earthquake and tsunami triggered the world's worst nuclear accident in 25 years at the Fukushima Daiichi plant northeast of Tokyo.
Resource-poor Japan relies heavily on energy imports from the Middle East and until recently met one third of its electricity needs with nuclear power, but now plans also to boost renewables such as solar and wind power.