(CNN) -- The Pentagon expects to get a read on Thursday from Afghan President Hamid Karzai on what he expects from the U.S. military going forward, a defense official said.
"We're going to tell them where we think it's going as far as training the Afghan National Security Forces, and they'll tell us where they think it's going," the official said.
Karzai's visit will cover the residual troop presence following the planned withdrawal of American combat forces in 2014 as well as negotiating an end to the war, another U.S. official said.
That official said reconciliation talks have "shown some signs of life after being dormant for the past year.
It is still a matter of getting a lot of stakeholders on the same page. The official said that includes the United States, Pakistan, the Afghan government and some factions of the Taliban.
Karzai's visit will include meetings with Defense Secretary Leon Panetta and other senior officials and a visit to the Pentagon's 9/11 Memorial.
He will not meet with former Sen. Chuck Hagel, who is President Barack Obama's pick to succeed Panetta and is working at the Pentagon to prepare for his Senate confirmation hearing.
A U.S. official with knowledge of the planned talks adds that policy officials will brief the White House at the end of the day "on the discussions, and convey any special issues which come up during the talks."
That briefing, along with a similar one from State Department officials also meeting with Karzai, will inform Obama's discussions with the Afghan leader on Friday.
The United States is considering a range of options for keeping troops in Afghanistan after the end of combat in 2014.
Karzai has said he would like for American forces to remain following the NATO mission.
An original plan recommended by Gen. John Allen, the commander of U.S. troops in Afghanistan, recommended between 6,000 and 15,000 troops to help with training and counterterrorism.
But that figure has been lowered to a suggested range of between 2,500 and 9,000, according to defense official.
"The military prefers the higher number," one official said.
The official said there the "low number option" of 2,500 that is being considered that would allow troops to perform a small training mission centered in a limited area, not spread throughout the country.
"The footprint would be too small and we wouldn't have much operational capacity with that number" for big counterterror missions, the official says.
Any number of remaining troops would have to include manpower to handle medical needs, food and equipment supply, maintenance, and transportation to allow forces to move around Afghanistan, the defense official said.
The Obama administration also has raised the possibility of pulling all troops out of Afghanistan at the end of next year.
The numbers game being played appears to be a series of trial balloons to gauge public reaction by the White House, and well timed to send Karzai, often a thorn in the administration's side when it comes to a U.S. troop presence, a message he may not get everything he wants.
As one senior Capitol Hill staffer with knowledge of the administration discussions said we will see the White House "float wildly low and wildly high numbers as trial balloons for a week or so before they leak the president's middle ground," numbers they consider to be a responsible option just days before an official announcement.
Regardless, the numbers still drive a debate. There is a view for a smaller troop presence.
One of the most vocal arguments against the administration's numbers comes from Afghan war policy experts Frederick and Kimberly Kagan.
"At the force level the administration has suggested, the U.S. would be able to keep only two bases in Afghanistan, most likely for logistical reasons," they wrote in an opinion piece in Wednesday's Wall Street Journal.
The Kagans also say a reduced troop presence would most likely restart the civil war that raged until the U.S. invasion in 2001.
"Warlords will begin fighting each other and the insurgents and terrorists in ungoverned spaces. The conditions will be ideal for al Qaeda's return," they said.
Afghan lawmakers have been vocal about the reduced numbers as well.
"If Americans pull out all of their troops without a plan, the civil war of the 1990s would repeat itself," Naeem Lalai, an outspoken lawmaker from volatile Kandahar province told Reuters on Wednesday.
Mark Jacobson, a former NATO adviser to then-U.S. commander in Afghanistan, Gen, David Petraeus, said numbers under 6,000 troops would make it impossible to conduct any kind of mission in the country.
But Jacobson says the numbers being floated are also a shot across Karzai's bow.
"Karzai's people have said the U.S. needs Afghanistan more than Afghanistan needs U.S. troops and the administration is less than pleased with that," Jacobson said.
U.S. defense officials are playing a wait-and-see game on what the Karzai visit will produce.
A Republican member of the Senate Armed Service Committee, Lindsay Graham of South Carolina, said on Sunday that he would like to see a much larger enduring U.S. troop presence in Afghanistan.
Graham's comments represent what the opposite side of the spectrum, generally embraced by Republicans.
"I think somewhere in the 15,000 to 20,000 range, depends on what the military commanders say," Graham told CNN's Candy Crowley on State of the Union
But Jacobson says we the numbers could also depend on how the Afghan government is perceived by the Afghan people. If the government seems to be providing basic services and has the support of the people, a reduced U.S. troop number could be appropriate.
Combined with a competent Afghan security force, there could be little reason to keep troops other than a U.S. counterterrorism force inside the country, according to Jacobson.