The claim from the environmental campaign group follows media reports suggesting the government plans to release the water into the ocean.
Many scientists say the risk is low but some environmentalists oppose the idea.
The government has not yet responded to the Greenpeace report.
For years Japan has debated over what to do with the more than a million tonnes of water used to cool the power station, which went into meltdown in 2011 after being hit by a massive tsunami.
Space to store the liquid - which includes groundwater and rain that seeps daily into the plant - will fill up by 2022.