Under the proposal, Japan's defense ministry is to cooperate with Australia in developing special steel and other materials for its new submarines, while Tokyo will be in charge of assembling them, the Mainichi Shimbun said.
The Australian side has taken "a positive stance" on the proposal, the daily said, adding that the two countries may strike a deal by the end of 2015.
Australia needs to replace its fleet of diesel and electric-powered subs, which date from the 1990s, and Japan's high-tech ship-building industry is thought to be well-placed to win the contract.
But opposition politicians and industry groups in Australia protest that losing the contract could deal a potentially fatal blow to naval shipbuilding at home, with a knock-on effect for associated industries.
However, critics point out that Japan may be able to supply the fleet for as little as half of the cost of making it at home.
Japan is on a drive to promote its manufacturing industries abroad, with Prime Minister Shinzo Abe touring the world as salesman-in-chief.
Abe has argued that Japan must play a bigger role on the global stage and has pushed to loosen post-World War II restrictions on when its well-equipped armed forces can act.
He has also relaxed a self-imposed ban on weapons exports, paving the way for the possible deal with Australia.
Immediate confirmation of the report was not available.