The government will pay 2.05 billion yen ($26 million) to buy islands known as Senkaku in Japan and Diaoyu in China.
There was no confirmation from officials, but the reports were carried by major Japanese media outlets, citing government sources.
The outspoken Tokyo governor had also been seeking to buy the islands.
Shintaro Ishihara had been collecting public donations for the purchase by the Tokyo metropolitan government, amid high tensions with China over the island chain.
At a regular press conference, Chief Cabinet Secretary Osamu Fujimura said the government and owner were in talks but would not comment on details of the discussion.
“We are negotiating with the owner while we try to grasp where the situation stands between [the central government] and the Tokyo metropolitan government,” he said.
An announcement would be made “when we reach a result after completing the process”, he said.
Kyodo news agency, citing government sources, said the agreement to buy three of the five main islands was reached with the owner on Monday.
A formal purchase contract would likely be exchanged by the end of this month, it said.
The cabinet will approve the deal in the middle of this month, both the Asahi and Yomiuri newspapers said.
The Japanese government says it has no plans to build on the islands, unlike Shintaro Ishihara who had suggested he could build a dock.
The purchase is likely to raise tensions with China, but less so than were Shintaro Ishihara to buy them.
Japan controls the islands, which lie south of Okinawa and north of Taiwan, but China also claims them, as does Taiwan.
Earlier this month, a group of Hong Kong activists landed on one of the islands amid the rumbling row. Japanese nationalists also subsequently visited, sparking protests in several Chinese cities.
On Tuesday, two men were held in Beijing for ripping the flag off the Japanese ambassador’s car, in an apparent protest over the islands.
The disputed islands sit in key shipping lanes and are thought to lie close to gas deposits.
On Wednesday an editorial in China’s Communist Party mouthpiece the People’s Daily accused Japan of acting in a two-faced manner over the islands.
“It will be difficult to improve the strained China-Japan relations if the Japanese government continues to adopt the two-faced approach of expressing goodwill on the one hand and allowing right-wing forces to kidnap the government and public opinion on the other hand,” it said.
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