In what became the world's worst nuclear disaster since Chernobyl in 1986, a 9.0-magnitude quake and tsunami in 2011 caused meltdowns at three of the Fukushima Daiichi plant's six reactors.
The water has built up because the plant's operator, Tokyo Electric Power Co (TEPCO), has to pour it over the three reactors to keep the melted uranium fuel at a safe temperature.
Groundwater flowing from the hills above the plant enters the reactor basements, where it mixes with highly radioactive debris. That gets pumped out and treated before being stored in tanks that are fast filling up.
Asahi Shimbun newspaper said large storage tanks on the site currently store about 1.05 million tonnes of processed water.
The paper said space limitations mean that by the end of 2020, a maximum storage capacity of about 1.34 million tons will be reached.
It cites utility officials saying the storage tanks would become full of processed water by summer 2022.
A panel of experts met on Friday for the first time in eight months to consider options to get rid of the water, Japan Today reported.
The newspaper said the panel was to consider strategies such as evaporation of the water and injection deep underground, in addition to a recommendation by Japan's nuclear regulator to release the treated water into the ocean.
But local fishermen are fiercely opposed to that, fearing negative publicity could destroy their business.
Last year, TEPCO said water treated at the site still contains radioactive materials that for years it has insisted had been removed.
TEPCO and government officials plan to start removing the melted fuel in 2021, and want to free up part of the complex currently occupied with tanks to build safe storage facilities for melted debris and other contaminants that will come out.
In addition to four other options including underground injection and vaporisation, the panel on Friday added long-term storage as a sixth option to consider.
Several members of the panel urged TEPCO to consider securing additional land to build more tanks in case a consensus cannot be reached relatively soon.
TEPCO spokesman Junichi Matsumoto told the Associated Press contaminants from the decommissioning work should stay in the plant complex.
He said long-term storage would gradually reduce the radiation because of its half-life, but would delay decommissioning work because the necessary facilities cannot be built until the tanks are removed.