Joe McGinniss, author of "The Rogue: Searching for the Real Sarah Palin" claims Palin slept with Rice while he was playing for the University of Michigan.
The book claims Rice was playing in Alaska while Palin was a television sports reporter in Anchorage.
The book says Rice, a former Laker, confirmed the encounter but did not go into details.
Palin's husband, Todd Palin released a statement slamming the book, saying it's full of lies, smears and innuendo.
The Republicans' 2008 vice presidential nominee and former governor of Alaska made no new reference on her Facebook account to McGinniss' book, although Sarah Palin previously mocked McGinniss for moving into a rented house next door to the Palin home.
The book also repeats allegations first published in The National Enquirer that Sarah Palin had an affair with Brad Hanson, Todd Palin's former business partner.
In a statement released through Palin allies, Hanson again denied the allegation, calling it a "complete and outright lie."
Appearing on NBC's "Today Show," McGinniss defended his reporting.
"I think I was as fair as I could possibly have been given the fact that she told all the people who were closest to her not to talk to me," he said.
The Associated Press contributed to this report.