In an interview with NBC, Mr Cheney said that when the book is published next week "there are going to be heads exploding all over Washington".
When viewing the Syrian threat in 2007, Mr Bush was still stung by "the bad intelligence we had received about Iraq's stockpiles of weapons of mass destruction" and backed other advisers who counselled a diplomatic approach instead, according to a copy of the book obtained by the "New York Times".
"I again made the case for US military action against the reactor," Mr Cheney writes. "But I was a lone voice. After I finished, the president asked, 'Does anyone here agree with the vice president?' Not a single hand went up around the room."
Mr Bush sought to exert diplomatic pressure to force Syria to abandon its secret programme but the Israelis bombed the site in September 2007.
Although he praises Mr Bush as "an outstanding leader", Mr Cheney, who was notoriously secretive during his time in office, discloses of number of rifts within Mr Bush's close circle of aides.
He wrote that George Tenet, the CIA director, resigned in 2004 just "when the going got tough" and at a moment that was "unfair to the president".
Colin Powell, Mr Bush's first Secretary of State, is subjected to withering criticism for allegedly undermining Mr Bush by privately expressing doubts about the Iraq war.
"It was as though he thought the proper way to express his views was by criticizing administration policy to people outside the government," Mr Cheney writes.
The former vice-president states that he pushed for Mr Powell's resignation, which was "for the best".
Mr Cheney also reveals that he wrote a resignation letter dated March 28, 2001 and told an aide to hand it to Mr Bush if he ever had a heart attack or stroke that left him incapacitated.
The former vice-president, who has suffered a number of heart attacks and has recently lost a dramatic amount of weight, Mr Cheney writes that he was unconscious for weeks after undergoing heart surgery last year.
During that period, he says, he had a long, vivid dream that he was living in an Italian villa, walking along stone paths to get newspapers and coffee.
"I did it because I was concerned... for a couple of reasons," he told NBC television in an excerpt of an interview that will air on Monday.
"One was my own health situation. The possibility that I might have a heart attack or a stroke that would be incapacitating. And there is no mechanism for getting rid of a vice president who can't function."
His autobiography, "In My Time: A Personal and Political Memoir," is to be published by Simon & Schuster on Monday.
In it, he brands Condoleezza Rice, Secretary of State after Mr Powell, as naïve for her attempts to draw up a nuclear weapons deal with North Korea. He says he often fought with White House advisers over softening the president's speeches on Iraq.
Regarding the contentious "16 words" about Iraq's supposed hunt for uranium in Niger that were included in Mr Bush's 2003 State of the Union address to lay down the justification for the impending invasion, Mr Cheney he saw no need to apologise for making that claim.
He writes that Miss Rice eventually came around to his view. "She came into my office, sat down in the chair next to my desk and tearfully admitted I had been right."
The books starts with Mr Cheney's account of the terrorist attacks of September 11th, 2001, when he led the government's response from a bunker beneath the White House while Mr Bush was in Florida and then on a plane bound for Nebraska.
Mr Cheney wrote that he did not want to make any formal statement to the nation that day. Perhaps recalling the notorious "I am in control here" statement of Al Haig, Secretary of State when President Ronald Reagan was shot in 1981, Mr Cheney viewed public silence as best.
"My past government experience had prepared me to manage the crisis during those first few hours on 9/11, but I knew that if I went out and spoke to the press, it would undermine the president, and that would be bad for him and for the country," he writes.
"We were at war. Our commander in chief needed to be seen as in charge, strong, and resolute - as George W. Bush was."