The government will set aside the cash to buy some 3 to 5 square kilometres (1.2 to 2 square miles) of land somewhere near the crippled plant, the Asahi Shimbun reported.
But finding a candidate site for the facility, which the government envisages using for 30 years, is a political challenge as no local authority has so far raised its hand.
Tokyo would like to use land in three heavily contaminated towns near the plant, said the paper, adding environment minister Nobuteru Ishiara will speak with local officials this weekend.
The mayors of the towns -- Futaba, Okuma and Naraha -- along with the governor of Fukushima prefecture Yuhei Sato, are believed to be concerned that the temporary site could easily become permanent.
A large area around the plant was evacuated in the weeks after the March 2011 disaster when a huge tsunami sparked reactor meltdowns.
While some areas are now deemed safe for residents to return to, many others remain off-limits, with scientists warning that certain spots may be uninhabitable for decades because of high radiation readings.
Buying up land in these areas could be one way that the central government breaks the present deadlock in which evacuees remain in temporary housing because they are unable to buy new land or a new house without selling their now-worthless home.
No one from the environment ministry was available for comment on the report.
As of the end of August, the total amount of contaminated soil and debris collected through decontamination efforts, in which the top layer of soil is stripped from the land, stood at 132,738 tonnes, about 80 percent of which is from Fukushima prefecture.
This contaminated waste is currently stored at waste incineration plants, sewage treatment plants and agricultural and forestry facilities nationwide.
Experts say a more long-term solution needs to be found because storage capacity at these facilities is reaching its limits.