The assertion is made in an upcoming book by U.S. investigative reporter Bob Woodward, who is associate editor of "The Washington Post."
In a preview report Friday, the newspaper said the book quotes a U.S. source as saying about Mr. Maliki, "we know everything he says."
Iraqi government spokesman Ali al-Dabbagh said that if Woodward's account is true, it reflects a lack of trust between the two governments.
U.S. National Security Advisor Stephen Hadley issued a statement Friday that made no reference to the allegation of spying on Iraqi officials.
Hadley took issue with claims that U.S. President George Bush did not publicly acknowledge problems in Iraq and was detached from a review of Iraq policy.
Hadley also disagreed with Woodward's assertion that the 2007 surge of U.S. troops was not the primary factor in reducing violence in Iraq.
According to the Post, Woodward says there were three additional factors, including what he calls "groundbreaking" covert techniques to track and kill insurgent leaders. He also credits the decision by Shi'ite cleric Moqtada al-Sadr to rein in his Mahdi army militia, and the action of Sunni groups that turned against al-Qaida in Iraq. Hadley argues that the surge of U.S. troops "enabled" the other factors.
Woodward's book, called "The War Within: A Secret White House History," is based on interviews with intelligence, diplomatic and military sources, as well as two interviews with President Bush. It is set for release Monday.
"The War Within" is Woodward's fourth book on the Bush administration and Iraq. Woodward is best known for his work, along with Carl Bernstein, uncovering the Watergate scandal that ultimately led to the 1974 resignation of U.S. President Richard Nixon.
Some information for this report was provided by AP and Reuters.
