The report follows talks in Tokyo on Wednesday between Japan's top negotiator on North Korean nuclear issues and U.S. special envoy Sung Kim.
A Japanese foreign ministry spokesman said he could not immediately comment on the report.
Kyodo reported that U.S. envoy Christopher Hill, in talks in North Korea earlier this month, agreed that Washington would not make verification of Pyongyang's uranium enrichment program or proliferation activities a condition of delisting.
Hill also agreed that first verification of the North's plutonium-related activities listed by Pyongyang in June would be conducted, Kyodo reported.
The United States agreed to continue food support begun in June and asked Japan to consider helping with such humanitarian aid, Kyodo said.
Prime Minister Taro Aso had been informed of the U.S. decision and that Sung Kim had apparently conveyed it to Japan's top negotiator on North Korean nuclear issues, Akitaka Saiki, in talks on Wednesday in Tokyo, Kyodo said.
Japan was prepared to accept the delisting but would decline the request for food aid, taking into consideration that it plans to extend economic sanctions on Pyongyang because of a lack of progress in settling a feud over Japanese citizens kidnapped to the North decades ago, it reported.
Washington said it would take North Korea off the terrorism list, bringing economic and diplomatic benefits, once a system had been agreed to verify Pyongyang's nuclear program.