Clinton said the same thing on Tuesday before a United Federation of Teachers crowd, saying "The answer is yes! I intend to run."
Clinton's formal announcement is expected early next year. She's running for the seat left open by Daniel Patrick Moynihan's retirement next year.
According to a new book about the first lady, Clinton and her advisers see the Senate race as Clinton's turn in the spotlight after having bailed out her husband and stuck by him.
"This is a race for redemption," her campaign adviser, Harold Ickes, told writer Gail Sheehy. "It's really that simple."
In light of her failed health care reform plan, Whitewater and the impeachment scandal, Ickes added, winning the Senate "would permit her supporters to say there was a lot more here than anybody thought: You guys were wrong!"
Sheehy's book, Hillary's Choice, says the possibility that Clinton might run for the Senate was raised as early as 1997, with the president himself thinking in 1998 that it was a good idea.
"She's really popular in New York, isn't she?" President Clinton told New York state Democratic chairwoman Judith Hope at a Long Island fund-raiser in August 1998. "Maybe she should run for office."
The anecdote was related by Hope to Sheehy. The president's comments came as he watched Mrs. Clinton give a speech during the height of the Monica Lewinsky scandal. She was repeatedly interrupted by applause.
Sheehy also reports that talk of Clinton running in her home state of Illinois also surfaced in November 1998, when Democratic Sen. Carol Moseley-Braun, was defeated.
New York Rep. Charles Rangel, an early supporter of Clinton's New York candidacy, "heard Illinois political leaders salivating over the prospect" and told Sheehy he asked Clinton, "Why not New York?"
Hope told Sheehy she had even mentioned the possibility to Clinton back in December 1997 at a White House Christmas party. Hope told Sheehy that Clinton "simply raised her eyebrows in mock humility and laughed."
Wolfson declined to comment on the book.
The timing of Sheehy's book, published by Random House, could not be better. It is expected to be in stores on Friday, barely a week after Clinton affirmed her intention to run for the Senate seat being vacated by Sen. Daniel Patrick Moynihan.
It is the latest of a half-dozen books published this year alone featuring the first lady's life story -- an indication of just how much interest there is. The others range from Hell to Pay, a highly critical book by former federal prosecutor Barbara Olson, to Rebels in White Gloves: Coming of Age with Hillary's Class -- Wellesley '69, by Miriam Horn.