The countries have "agreed to arrange a summit next week" in Beijing on the sidelines of the Asia-Pacific Economic Cooperation (APEC) forum, Japan's national broadcaster NHK said.
Private network Fuji TV had a similar story.
"Now that we have shared understanding toward a summit meeting, we will start making concrete arrangements for it," a Japanese government source was quoted as telling the broadcaster.
Tokyo has long been pressing for such a meeting but Beijing has resisted, with the two sides locked in a territorial dispute and still at odds over World War II history.
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It has also been calling for Japan to acknowledge the existence of a dispute over the Tokyo-controlled Senkaku islands, which it calls the Diaoyus, where paramilitary vessels from both sides have sparred over recent years.
Japan has until now rebuffed the calls, but similarly worded statements issued Friday suggested there had been some accommodation on the thorny island issue, although it appeared to fall short of an explicit acknowledgement.