Quoting informed sources, the reports say that the EU plans to exempt vegetables, fruits other than persimmon, and livestock products from mandatory radiation checks.
Food imports from the region surrounding the Fukushima Daiichi nuclear plant have been subject to mandatory radiation checks since a disaster there in 2011.
Rice and some other foods produced in other prefectures might also be removed from the list, as will some edible wild plants.
The sources said the EU had approved a proposal to ease restrictions last week after an analysis of produce was performed by European scientists.
The executive arm of the EU is expected to officially decide on the deregulation measures by the end of this year.
Japanese ministers have put on a strong front in pursuing a scrapping of import restrictions. Most recently, foreign minister Fumio Kishida raised the subject with Federica Mogherini, his EU opposite number, in Luxembourg last month.
Japan hopes to increase its food exports by more than one-third by 2020. Currently, Europe accounts for just 5.4% of Japan’s overall exports, though this figure has increased by almost one-fifth over the last year.
If the European restrictions are eased, this will send a strong message to other countries over the safety of Japanese exports. Neighbouring South Korea currently bans the import of some Japanese fishery products, while Taiwan has been strengthening its import regulations for the country.