Rakuten is preparing to make a capital injection in AisAsia's Japanese unit, possibly in 2015, the Toyo Keizai economic magazine said on its online edition.
Two or three more Japanese companies may also put cash into AirAsia Japan, it said.
Shares in Rakuten were up 3.45 percent to 1,316 yen in early afternoon trade on the Tokyo Stock Exchange after the media report, which the company did not confirm.
The Toyo Keizai said one of the likeliest ideas was that Rakuten and AirAsia could hold a maximum one-third each of the Japanese unit's shares with the remaining one-third held by a combination of other Japanese firms.
AirAsia chief executive Tony Fernandes is likely to hold a news conference in Japan in early July, it said.
Public broadcaster NHK said talks were being held with the aim of Rakuten getting a stake of around 15-19 percent for a little more than one billion yen ($9.8 million).
Japan's aviation law limits a foreign equity stake in a Japanese airline to one-third.
The new carrier could operate flights linking central Japan's Chubu Centrair airport with main Japanese destinations, the Toyo Keizai said.
The magazine quoted a senior official at the transport ministry as saying it was aiming to start flight services in 2015.
AirAsia entered the Japanese market in 2012 in a joint venture with major carrier All Nippon Airways (ANA).
The venture ended in a spat over business practices last year. ANA has since inherited the business and rebranded it Vanilla Air. (AFP)
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