The radical move, considered in the fall of 2011 when Obama's re-election chances appeared uncertain, included extensive focus-group sessions and polling, says the book "Double Down," by journalists Mark Halperin and John Heilemann, due out Tuesday, Election Day.
The replacement idea was eventually abandoned when top aides Jim Messina, David Plouffe and William M. Daley, White House chief of staff at the time, concluded the move wouldn't help Obama's campaign enough to justify the change.
"When the research came back near the end of the year, it suggested that adding Clinton to the ticket wouldn't materially improve Obama's odds," the authors write in their book about the 2012 race.
"Biden had dodged a bullet he never saw coming -- and never would know anything about, if the Obamas could keep a secret," they say in the book, a sequel to "Game Change," which chronicled the 2008 campaign.
Daley, a major proponent of replacing Biden with Clinton, confirmed the book's account to The New York Times, which first reported on the book.
Daley, who was commerce secretary under President Bill Clinton, said he wanted to research what the move to Hillary Clinton would mean for Obama, whose popularity in fall 2011 was at its lowest in his presidency to that point.
Daley called the research "due diligence."
"I was vocal about looking into a whole bunch of things, and this was one of them," he told the Times.
"You have to remember, at that point the president was in awful shape, so we were like, 'Holy Christ, what do we do?'"
Biden, who may run for president in 2016, was viewed guardedly by Obama aides, the book says -- not just because of his gaffe-prone "Uncle Joe" image, but also because they saw him as excessively focused on his own political future.
The book says Biden viewed the 2012 campaign as a way of expanding his own donor network and laying the groundwork for his own possible presidential campaign four years later.
The authors say relations between Obama and Biden were difficult at times even during the 2008 campaign.
"How many times is Biden going to say something stupid?" the book quotes Obama as complaining during the first campaign.
Biden was also hurt by when Obama told a reporter it wasn't surprising he didn't recall a particular Biden quote.
Christie refused to endorse Romney early in the GOP presidential race and warned him against fundraising in New Jersey if he ever wanted Christie's support, the book says.
Romney was annoyed by this -- and said the warning like something out of "The Sopranos" TV drama, which was about a New Jersey mobster.
Despite the feelings, Romney's fundraising team largely complied with Christie's request, the book says.