The administration official told CNN the president was not satisfied with the proposals and specifically cited concern over an exit strategy. Obama met with his security team Wednesday in the Situation Room.
In another major development Wednesday, the U.S. ambassador to Afghanistan is said to have expressed concern to Obama about sending more troops to the region until the government in Kabul deals with corruption and mismanagement.
Previous media reports had indicated five options were on the table. Although the options aren't being developed, one has become fairly fleshed out, CNN said.
That option calls for sending about 34,000 U.S. troops to Afghanistan, deployed mainly in the south and southeast, where much of the fighting is, a senior administration official and U.S. military official independently confirmed for CNN. The plan reportedly would include three Army brigades, a Marine brigade, a headquarters element and support troops.
The other options, the Pentagon official said, would be "different mixes," or "different components of it."
Obama also is expected to discuss the kind of cooperation the United States could expect from Afghan President Hamid Karzai, the type of civilian support the United States would be willing to provide and the kind of support the United States could expect from other countries, the administration official told CNN.
"The president will have an opportunity to discuss four options with his national security team," Press Secretary Robert Gibbs told reporters.
Gibbs said the timeline for Obama's decision remained fluid.
"Anybody that tells you that the president has made a decision or ... 'tentatively agreed to' doesn't have, in all honesty, the slightest idea what they're talking about," Gibbs said during Tuesday's briefing. "The president has yet to make a decision."
The U.S. ambassador to Afghanistan has expressed concern about sending more troops to Afghanistan until the government in Kabul can clean up corruption and deal with mismanagement that has helped the Taliban regain strength, The Washington Post reported Wednesday.
Citing senior U.S. officials, the newspaper said Ambassador Karl W. Eikenberry registered his concern in two classified cables to Washington within the past week.
Eikenberry was the U.S. military commander in Afghanistan in 2006 and 2007. He retired from the military in April when he was sworn in as ambassador.
In the cables to Washington, Eikenberry said Afghan President Hamid Karzai had engaged in erratic behavior and senior Afghan government officials were corrupt, the Post reported.