Aso and Zhang chatted for "minutes" on the sidelines of the Asia-Pacific Economic Cooperation (APEC) finance ministers' gathering in Beijing, ahead of the forum's annual summit next month, according to Japanese media.
"This was meant to be a step toward making the final arrangements for a Japan-China summit," the Nikkei said.
Aso also serves as Tokyo's finance minister.
Japanese Prime Minister Shinzo Abe has been pushing for his first meeting with Chinese President Xi Jinping.
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But the two sides have made visible steps in recent weeks towards a possible Abe-Xi summit.
Abe made brief contact with Chinese Prime Minister Li Keqiang last week on the sidelines of an international gathering in Italy, followed by other meetings between senior officials and a visit to China by a major Japanese business delegation.
The Japanese business community has been watching with keen interest whether Beijing and Tokyo can use APEC as an opportunity to ease tensions, if not to reset ties.
The purchase prompted angry anti-Japan protests in China, where Japan Inc. Has faced greater difficulties doing business than before.
Coastguard units from Japan and China now routinely play cat and mouse around the islands as both sides seek to assert sovereignty.
Beijing also sparked regional controversy -- as well as condemnation from Washington -- late last year with its unilateral declaration of an Air Defence Identification Zone which overlaps the islands.
He made an offering to the shrine last week.