The book said Jobs reacted angrily to the offer to help extend his life when he was suffering from pancreatic cancer.
"He cut me off at the legs, almost before the words were out of my mouth," said Cook, according to the book, "Becoming Steve Jobs," due to be released later this month by Brent Schlender and Rick Tetzeli.
Cook quoted Jobs as saying, "I'll never let you do that. I'll never do that."
Cook told the authors he was surprised by Jobs's reaction to the liver offer, according to excerpts of the book released by the magazine Fast Company.
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"I said, 'Steve, I'm perfectly healthy, I've been checked out. Here's the medical report. I can do this and I'm not putting myself at risk.'
The Apple co-founder later did receive a liver transplant in 2009. He died in October 2011 at age 56 after a long battle with cancer.