It may also just withdraw all U.S. troops by the end of the year, the Wall Street Journal reported.
The possibility of waiting reflects an increasing Pentagon and White House belief relations with Afghan President Hamid Karzai will not improve and he probably won't sign the bilateral security agreement, or BSA, with the United States before Afghanistan's presidential elections in April, the Journal said.
"If he's not going to be part of the solution, we have to have a way to get past him," a senior U.S. official told the newspaper. "It's a pragmatic recognition that clearly Karzai may not sign the BSA and that he doesn't represent the voice of the Afghan people."
White House, Pentagon and Afghan officials had no immediate comment on the report.
The Pentagon's latest proposal is to keep 10,000 U.S. troops in Afghanistan at a few bases to act as a stabilizing presence after the presidential election, the Journal said. A separate limited advisory mission would train Afghan security forces.
The 10,000-member force would be drawn down over two years, with the intent that all U.S. troops would be out of Afghanistan by the end of the Obama administration except for military personnel who would work in a defense office at the U.S. Embassy in Kabul.
Washington insists Afghanistan approve the BSA before it will agree to leave the troop contingent behind. But Karzai so far has refused to sign the accord.
Among his stated reasons, he has said Washington should be responsible for persuading the Taliban to talk to the Afghan government. He has also balked at providing prosecution immunity to the U.S. troops that remain in Afghanistan after 2014.
In refusing to sign the pact, Karzai has said his successor should make the decision.
A senior U.S. official told the Journal Karzai is playing a "game of chicken" with the White House.
"We're just pulling our car off the side of the road," the official said.
The White House has said Karzai's refusal to sign the accord may lead President Obama simply to order a complete U.S. troop withdrawal this year, the Journal said.
The Afghan government had no comment on such a prospect.
Voting in Afghanistan's presidential election is scheduled for April 5.
Ashraf Ghani Ahmadzai, a former finance minister and chancellor of Kabul University, is ahead in the polls among 11 contenders.
But no single candidate appears likely to win more than 50 percent of the vote, so a second round looks likely, the Journal said.
This means a new government is unlikely to take office before August.
At that point, the Pentagon plans to be prepared either to keep 10,000 troops in Afghanistan post-2014 or pull all of the troops out by year-end, officials told the Journal.