Cheney, 70, said he wrote the letter because "there is no mechanism for getting rid of a vice president who can't function." He had his fifth heart attack during President George W. Bush's administration.
"There are gonna be heads exploding all over Washington" when his book, "In My Time," hits bookshelves, Cheney told NBC in an exclusive interview that will air Aug. 29, the day before the book's release.
The book covers the Sept. 11, 2001, attacks and his opinions of Bush and former Secretaries of State Condoleezza Rice and Colin Powell, MSNBC reported Wednesday.
Cheney writes he has no regrets over the use of so-called enhanced interrogation techniques, including waterboarding, used to extract information from terror suspects.
"I would strongly support using it again if we had a high-value detainee and that was the only way we could get him to talk," Cheney told NBC.