The New York Times said on Monday that Pentagon officials link the reduction to progress made in fighting anti-US military operations in Iraq and in training Iraqi security forces.
Officials, however, remain cautious, noting that there are still between 12,000 and 20,000 fighters in Iraq.
Attacks on US-led forces in Iraq have dropped to between 30 and 40 a day from a high of 140 a day before the 30 January elections.
And attacks now are mostly aimed at Iraqi civilians and security forces, according to the Times.
"We're on track," General Richard Myers, the chairman of the
Joint Chiefs of Staff, told the newspaper.
He warned, however, that fighting in Iraq "kills virtually every day", and that it is "still a very potent threat".