"He doesn't want to lose the gains we have made," said the military officer who, like others, spoke on condition of anonymity because the report is still being developed.
Some officials say they expect Petraeus to push for maintaining the current force level for at least six additional months to build upon security improvements in Baghdad.
U.S. force levels reached nearly 162,000 this month, an increase of about 30,000 from the beginning of the year, when the American military's troop buildup began.
Another Defense official, who has been part of Iraq planning but skeptical of the troop increase, said moving forces out of Al Anbar could make sense to the White House, because doing so would enable the administration to show that improved security translates into a reduction in troops.
Cutting the number of troops in Al Anbar would also eliminate the need to request more forces to secure areas around Baghdad, where the U.S. has been focusing much of its military effort.
"If the Marines are having so much success in Al Anbar, maybe we redeploy them to some other hot spot," said the Defense official. Administration officials have cited improved ties with Sunni Arab leaders in Al Anbar with helping reduce violence and curb the power of the insurgents.
Not all military commanders favor reducing the number of troops in more stable areas. In a news conference last month, Marine Maj. Gen. Walter E. Gaskin, the commander of U.S. forces in Al Anbar, cautioned against cutting back forces there too quickly.
Gaskin argued that the added forces had allowed the Marines to eliminate havens used by the insurgent group that calls itself Al Qaeda in Iraq.
A "persistent presence" of U.S. forces, he said, would help give Iraqi security forces more experience and confidence, and the ability to keep militants out.
"It takes time to gain experience," he said. "I see that experience happening every day, but I don't see it happening overnight. I believe it's another couple of years in order to get them to do that -- and that's not a political answer, that's a military answer."
But division and brigade commanders in other parts of Iraq have said they anticipate recommending further reductions in the months to come. Army Maj. Gen. Benjamin R. "Randy" Mixon, the American division commander for northern Iraq, said last month that he expected to cut the number of troops in his area, but emphasized that reductions should be made slowly.
