US defence chief Robert Gates is seeking support from politicians on a draft deal to extend the US mandate in Iraq, which expires later this year.
Details have not been released, but officials say it would see US troops withdraw from Iraq by the end of 2011.
Mr Gates is said to be briefing key members of Congress on the deal, although their approval is not needed.
But the draft does need approval on the Iraqi side, which correspondents say could prove difficult.
The current UN mandate for US-led coalition forces in Iraq expires on 31 December. About 144,000 of the 152,000 foreign troops deployed there are US military personnel.
US officials say the deal would see combat forces withdrawn from Iraqi towns and cities by the middle of 2009, and could see US troops withdraw completely by the end of 2011.
However, a Pentagon spokesman said the complete withdrawal "will only be followed if the conditions on the ground provide for it".
The Bush administration has long opposed the idea of a timeline for the withdrawal of US troops.
Mr Gates, Secretary of State Condoleezza Rice and President George Bush's national security adviser, Stephen Hadley, are said to be reaching out to key members of the House of Representatives and the Senate.
Ms Rice also is also said to be pressing senior Iraqi leaders to accept the deal.
The first test for the agreement is at a meeting of the Political Council for National Security on Friday.
The body brings together all the top Iraqi political figures, including the heads of parliamentary blocs.
If it wins approval there - and that's not expected to be automatic or trouble-free, says the BBC's Jim Muir in Baghdad - that would imply that endorsement by parliament, and the cabinet should follow on relatively smoothly.
Senior Iraqi officials involved in the negotiations say they believe all the outstanding issues have been settled.
The Iraqi government believed that the current immunity from prosecution by granted to US troops and contractors by the former Coalition Provisional Authority (CPA) undermined Iraqi sovereignty.
The new draft is said to grant Iraqi judicial authorities limited ability to try US troops and contractors for major crimes committed off-duty or off-base - if a joint US-Iraqi committee agrees.
It is a move that worries some members of the US Congress.
"I am sceptical of any agreement that would subject US servicemen and women to the jurisdiction of Iraqi courts in the middle of a chaotic war," Senator Carl Levin, chairman of the Senate Armed Services Committee, told the Associated Press.
However, a US spokesman said Mr Gates believed it offered adequate protection for US forces in Iraq.
Another difficulty that remains is that any agreement for the continuing presence of US troops in Iraq is anathema to some of the political groups in Iraq, our correspondent says.
The faction loyal to the militant Shia cleric, Moqtada Sadr, is bitterly opposed and a big protest demonstration has been called for Saturday.
If there is no final agreement by the end of the year, the two sides would have to go back to the UN to renew its mandate.
seeking 尋找;探索;追求 企圖,試圖
approval 批准;認可 贊成;同意
correspondents 通訊記者;特派員 通信者
coalition 結合,聯合 (政黨、國家等)臨時結成的聯盟
forces 力氣 暴力 影響;支配力;說服力 軍事力量;軍隊
administration 管理,經營;監督 施行,實施,執行
Immunity 免疫力;免疫性 免除,豁免 豁免權
Representatives adj 代表性的,典型的 noun 典型,代表物 代表,代理人
imply 暗指;暗示;意味著 必然包含;必需
endorsement 背書;簽署 贊同;支持
involved 使捲入,連累;牽涉 需要,包含,意味著
judicial 司法的;審判的 評判的;公正明斷的;公平的
joint 聯合的,共同的 連接,接合
jurisdiction 司法;司法權,審判權,裁判權 權力;管轄權
adequate 能滿足需要(量)的,足夠的 勝任的