An agreement would allow arms shipments to countries involved in international conflicts but still prohibit exports to countries sponsoring terrorism or violating international ammunition treaties, the newspaper said.
The ruling Liberal Democratic Party is not guaranteed to get the approval of its main coalition partner, New Komeito, the report said.
The newspaper said talks between Liberal Democrats and New Komeito members could run into difficulties since the pacifist-leaning Komeito remains cautious about lifting the ban.
Up for discussion will be how to control weapon uses after they have been exported, and what weapons won't be exportable.
If approval is gained, the beneficiaries would include Japan's high-tech and heavy manufacturing companies, including Mitsubishi Heavy Industries, IHI Group and Kawasaki Heavy Industries.
Japanese businesses could bid for more major arms deals and technology transfers at home and abroad.
Winning contracts would improve competitiveness of Japanese businesses and keep manufacturing and development costs down for new equipment, proponents said.
In particular, Mitsubishi is in talks to take on more manufacturing of Japan's deal for Lockheed Martin F-35 Lightning fighter jets.
But increased arms exports could further deteriorate relations with Japan's Southeast Asian neighbors -- especially China -- over maritime territorial disputes, observers say.
The Cabinet of Prime Minister Shinzo Abe approved a national security strategy in December that would boost spending on military equipment.
The strategy, which includes the revised National Defense Program Guidelines and a Mid-term Defense Program, could start the export of weapons from Japan for the first time since World War II.
The guidelines call for a revision of a pillar of Japan's postwar pacifism -- the export of weapons under the new principle of "a proactive pacifism," the Asahi Shimbun reported when the documents were released in December.
Japan has limited the export of weapons under a 1967 self-imposed embargo. Exports were banned to Communist countries, nations under U.N. Security Council arms embargoes and governments involved in international conflicts.
Over the years exceptions have been made, starting in 1983 with a technology transfer deal to the United States, the newspaper said.
Japan already is committed through the Mid-Term Defense Program, released in December, to boost spending on military personnel and equipment.
The strategy increases spending by just under $10 billion over five years to $391 billion starting next year and increases the number of military personnel.
At the top of Japan's military shopping list -- apart from the Lockheed Martin F-35 -- are four new early-warning aircraft and three new air-refueling and transportation aircraft.
Japan also is looking at new Bell Boeing Osprey tilt-rotor aircraft and Northrop Grumman RQ-4 Global Hawk surveillance drones, the report said.