The 3,000 would be part of a "training mission" with the Iraqi military, and that considerably small number would be "more than adequate" for the task, the officials said.
About 46,000 U.S. troops are in Iraq now. At the beginning of August, Iraqi leaders announced that they would begin negotiations with the U.S. to keep a residual force in Iraq. Under a 2008 security agreement between Washington and Baghdad, all U.S. troops are slated to leave by Dec. 31.
Continued instability and fear of growing Iranian influence in Iraq prompted some Iraqi and U.S. officials to reconsider the deadline.
The 3,000 figure reflects "reality" in Iraq and in the United States, the administration officials told NBC News, denying reports of any deep divisions among the White House, Pentagon and State Department.
But The New York Times said the number would be far less than that recommended by American commanders in Iraq. It also noted that President Barack Obama had long pledged to withdraw all U.S. forces by the deadline, and leaving a few thousand troops in Iraq would break that promise.
Considering the U.S. political climate, it would be difficult for Obama to leave large numbers of U.S. military forces there when the U.S.-Iraq agreement on troop presence expires, one official said. At the same time Iraqi Prime Minister Nouri al-Maliki is under "tremendous pressure himself" to send the American forces packing, the official said.
The officials told NBC News that the discussions about the level of American forces in Iraq after this year started with a "broad range" and "somewhere between 10,000 and 20,000" when it was unclear what exactly their mission would be. But once negotiations with the Iraqis got under way and the role was narrowed to a "training mission," it was determined that 3,000 would be sufficient, they said.
On Tuesday, Defense Secretary Leon Panetta was quoted by Fox News as saying "no decision has been made" on the final number of troops to stay in Iraq.
"That obviously will be the subject of negotiations with the Iraqis and as a result of those negotiations. As I said no decision has been made of what the number will be," he said.
Fox News said Panetta had already signed off on the 3,000 figure and that senior commanders disagreed.
"We can't secure everybody with only 3,000 on the ground nor can we do what we need to with the Iraqis," Fox News quoted one source as saying.
White House press secretary Jay Carney at his press briefing Tuesday afternoon flatly denied the Fox News report, NBC News reported.
"We are operating under a status of forces agreement with the Iraqi government that was signed by the previous administration to draw down our forces," Carney said. We are in negotiations, consultations with the Iraqi government about what our relationship with Iraq will look like going forward.
"We want a normal, productive, healthy relationship with Iraq," he said. "If the Iraqi government makes a request of us, we will certainly consider it."
But for the time being, Carney added, the two countries are continuing to operate "under existing agreements."
Asked about budgetary restraints weighing on troop-strength decisions, Carney acknowledged that "we live in a world ... where resources aren't finite," Politico reported.
Sens. John McCain, R-Ariz., Joe Lieberman, I-Conn., and Lindsey Graham, R-S.C., issued a statement Tuesday that they were "deeply troubled" about the drawdown level.
"This is dramatically lower than what our military leaders have consistently told us over the course of repeated visits to Iraq that they require, and that is needed to support Iraq in safeguarding the hard-won gains that our two nations have achieved at such great cost," they said in the statement obtained by NBC News.
"In particular, we are very concerned by the prospect that a follow-on force might lack the capabilities and authorities necessary to help Iraqis ensure stability across the disputed territories in northern Iraq, which we consider an essential mission," the three said.