Bush is expected to let one Marine battalion, numbering about 1,000 troops, go home on schedule in November and not replace it, but he otherwise would keep in place the current combat force.
At the same time, the president is expected to announce more troops will be coming back home after the first of the year. By January the drawdown would amount to between 7,500 and 8,000 troops, including the departure of one Army combat brigade, numbering between 3,500 and 4,000 troops.
The plan also would send a small Marine contingent to Afghanistan in November to replace one of two units scheduled to head home then.
Bush is scheduled to announce the plans during remarks Tuesday at the National Defense University in Washington. White House officials said Monday that the president was nearing an announcement but declined to comment beyond that.
Officials familiar with the president's likely announcement described it on condition of anonymity because of the sensitivity of the matter.
Despite waning clout in the final stretch of his presidency, Bush has remained able to run the war on his terms, deciding troop levels as he sees fit.
That includes this latest announcement, in which Bush is largely maintaining the current force level in an effort to hold onto hard-fought security gains in Iraq.
It well could be his final major decision on the U.S. troop posture in Iraq as president.
The new plan may disappoint some members of Congress and others who expected a larger, faster reduction of troops in Iraq, considering the significant downturn in violence. According to defense officials, violence has plunged by about 80 percent since last year's peak.
Gen. David Petraeus, the top U.S. commander in Iraq, delivered his recommendations to military leaders about two weeks ago.
As Bush's plan shapes up, it would be left to the next president to execute further troop reductions in Iraq and a greater buildup in Afghanistan. Several more combat brigades are scheduled to leave Iraq during the first half of next year, and decisions must be made on whether or not to replace them.
Commanders repeatedly have asked for more troops in Afghanistan, where there has been a resurgence of the Taliban and a growth in violence.
Anthony Cordesman, an Iraq expert at the Center for Strategic and International Studies, said the emerging plan reflects the concern of U.S. commanders: Rushing U.S. force reductions could lead to instability at a pivotal time of Iraqi political progress and preparedness of Iraqi forces.
"This plan does, however, mean continuing stress on both the active and reserve forces," Cordesman added.
Bush's term ends Jan. 20.
Democratic presidential nominee Barack Obama has advocated pulling all U.S. combat forces out of Iraq within 16 months of the new president taking office. GOP nominee John McCain has said he would rely on the advice of U.S. military commanders to determine the timing and pace of troop reductions.
Associated Press writers Lolita C. Baldor and Robert Burns contributed to this report.