Japan's two-year mission is due to expire on December 14.
A Kyodo News report said the Japanese government told a ruling party leader that the mission will be extended by a full year to provide leeway, however a May date is being considered for withdrawal.
Japan's Cabinet will decide next week on how long troops will remain, said the report.
Around 600 Japanese troops are based in Samawah to train Iraqi security forces, in the country's first military deployment since World War II to a nation where fighting is underway.
Japan's pacifist constitution restricts troops to non-combat operations, however the deployment is increasingly unpopular in the country, at a time when close ally the United States is facing mounting calls for a swift pullout from Iraq.
A spokesman for Prime Minister Junichiro Koizumi would not confirm the report, but said the issue would be dealt with soon.
The Mainichi Shimbun newspaper said the government decided on the withdrawal timetable due to the uncertain security situation in Iraq but on the assumption that the country's new government will be operating smoothly by late 2006.
Jiji Press earlier reported that Japan plans to keep deliberating on when to end its troop deployment even after extending the mission for a year.
The ruling Liberal Democratic Party on November 22 proposed the first ever revision of the constitution that would recognize Japan has a military, paving the way for more peacekeeping operations overseas.
Meanwhile a poll, published by the national Asahi newspaper on Tuesday, showed 69 percent of those interviewed opposed extending the mission, and support for it fell to 22 percent.