Obama's revised strategy is also expected to include timelines for training Afghan army and police units to eventually take security responsibility from U.S. and NATO forces.
A transition to greater Afghan control could begin within the next year in parts of Afghanistan that are more stable, including the city of Herat near the Iranian border.
Obama has said he hopes to wrap up the U.S. military mission in Afghanistan before handing off to the next president -- a window of between three and seven years, depending on whether he wins a second term in 2012.
Afghan President Hamid Karzai has said Afghanistan's army and police should be ready to take over security from Western forces within his new five-year term.
Defense Secretary Robert Gates has said an eventual drawdown in Afghanistan could follow the Iraq model, whereby U.S. forces would pull back and eventually out of city centers.
But Gates has cautioned against putting a specific date on the U.S. military's exit, saying that depended in large measure on the conditions on the ground.
The counterinsurgency strategy proposed by Gen. Stanley McChrystal, the top U.S. and NATO commander in Afghanistan, is expected to be combined with a stepped up counterterrorism campaign, advocated by Vice President Joe Biden, using unmanned aerial drones and special operations forces to combat Taliban and al Qaeda fighters along the Afghanistan-Pakistan border.
The United States wants Pakistan to crack down on Taliban leaders and their allies organizing the insurgency from safe havens there, including the network headed by veteran Taliban commander Jalaluddin Haqqani. Islamabad has been reluctant to do so in the past, U.S. officials say, citing long-suspected links between the Haqqanis and elements of Pakistani intelligence.
Administration officials say Obama wants greater outreach to groups that fight alongside the Taliban but could be persuaded to lay down their weapons in exchange for a greater role in local governance.
Several of Obama's top national security and military advisers, including Defense Secretary Robert Gates and Admiral Mike Mullen, chairman of the Joint Chiefs of Staff, have coalesced around two final options -- deploying 30,000 to nearly 40,000 additional troops to Afghanistan, officials say.
If bolstered by trainers from NATO allies, these two options would largely give McChrystal the 40,000 additional troops that he recommended to try to stem Taliban gains.
At that level, McChrystal estimates, he would be able to focus on securing Afghan population centers and would have some additional resources to move against Taliban and al Qaeda fighters in outlying areas, officials said.
Discussions have focused on sending two additional brigades, totaling between 10,000 to 15,000 troops, to southern Afghanistan around Kandahar, a key Taliban stronghold.
Another brigade was also likely to be added in eastern Afghanistan near the border with Pakistan.Brigades range in size but generally include 3,500 to 4,000 troops. They can swell to over 5,000 troops if other units are attached to them. Marine brigades can be larger.
The leading military alternative to the larger buildup calls for sending just 20,000 additional troops to Afghanistan. That may be more politically palatable for Obama and his Democratic allies in Congress. It would allow McChrystal to accelerate the training of the Afghan army and police but would provide him with few additional resources for a broader campaign against the Taliban.
The smallest increase on the table would send another 10,000 to 15,000 troops to focus on training Afghan forces.
ANTI-CORRUPTION 'COMPACT' WITH AFGHAN GOVERNMENT
A key part of the emerging strategy would be a compact, or commitment, by Karzai's government to crack down on corruption and improve governance.
U.S. officials say getting Karzai to do so is critical to a successful counterinsurgency that hinges on Afghans supporting their government instead of the Taliban.
U.S. officials are divided on the prospects of success. Mullen supports a large troop increase but has described Karzai's legitimacy after August's fraud-marred election as at best, in question right now and, at worst, doesn't exist.
In contrast, the U.S. ambassador to Afghanistan, Karl Eikenberry, has expressed deep concern about sending more troops until Karzai demonstrates a greater willingness to tackle corruption and mismanagement.
Gates sees no quick-fix to these problems and has suggested that the United States could threaten to withhold some aid contracts to pressure Karzai's government to act.
PAYING THE BILLS
Obama has asked his advisers for cost estimates for expanding the war in Afghanistan, exposing divisions between the White House and the Pentagon on an issue that could have political consequences for Obama in the run-up to next year's congressional elections.
The White House Office of Management and Budget estimates that it will cost about $1 million for each additional soldier sent to Afghanistan. That means a 30,000 to 40,000 troop surge would add approximately $30 billion to $40 billion a year to the war's already soaring cost.
The Pentagon's comptroller has, in contrast, estimated the operating cost of deploying and sustaining one additional soldier for a full year in Afghanistan at half that amount, or roughly $500,000.
Budget experts say putting a precise price tag on a proposed troop increase at this stage in the review process is virtually impossible. Costs depend on a number of factors, such as what types of equipment and units are sent, that have yet to be decided. Helicopter squadrons, for example, are far more expensive than infantry units.
War spending in Afghanistan has more than doubled over the last year, reaching $6.7 billion in June alone, and Pentagon officials worry that sticker shock could fuel congressional opposition to Obama's expected buildup. (Reporting by Adam Entous; Editing by Jackie Frank)