The book, "The Story of Watergate's Deep Throat," says Felt hastily withdrew his denial when a Justice Department official reminded him he was under oath, according to the newspaper, which said it obtained a copy from a Virginia bookstore that mistakenly put copies out for sale.
Former FBI official Mark Felt, who is now 91, came forward in May as Woodward and Carl Bernstein's infamous deep background source. The information he gave about the 1972 burglary of Democratic Party offices at the Watergate in Washington, D.C., led to President Nixon's resignation in 1974.
The book is due in stores next Wednesday.
According to USA Today, the book says Woodward suspected that someone at the Post was leaking information about his sources to the Nixon White House. No leaker was found.
The book also identifies the garage where Woodward and Felt, a high-ranking FBI official, conducted their clandestine late-night meetings. The garage is "behind and underneath" 1401 Wilson Boulevard in the Rosslyn section of Arlington, Va., Woodward wrote.
The building is near several large apartment towers in a section of Arlington that is a very short drive to downtown Washington, D.C.
In the grand jury incident, Woodward wrote that Felt's actions enabled the Justice Department official who was questioning him to realize that he had been "Deep Throat."
A grand juror asked whether Felt was "Deep Throat" and Felt replied, "No."
The Justice Department official, Stanley Pottinger, offered to have the question and answer withdrawn as being outside the bounds of the investigation, after reminding Felt that he had sworn to tell the truth.
"Flushed," Woodward writes, "Felt very rapidly requested, 'Withdraw the question."'
Pottinger did not reveal what he had figured out because he did not think it appropriate to divulge a reporter's confidential source, Woodward wrote.
Woodward wrote that Felt was motivated by a desire to protect the FBI, disgust with the Nixon White House, reverence for former FBI Director J. Edgar Hoover and the thrill of "the game."