WASHINGTON (Reuters) - President George W. Bush believes Democrat Hillary Clinton will win her party's presidential nomination but that the Republican nominee will beat her in the November 2008 election, a new book said.

"She's got a national presence, and this is becoming a national primary," Bush said in an interview for "The Evangelical President," a book by a reporter for The Examiner newspaper of Washington, Bill Sammon.

"And therefore the person with the national presence, who has got the ability to raise enough money to sustain an effort in a multiplicity of sites, has got a good chance to be nominated," he said.

Bush, whose public approval rating is about 30 percent, has generally kept out of the race to succeed him, saying he did not want to become "pundit in chief."

But he said at a news conference last week that he believes he will be a strong asset for Republicans in the 2008 race.

Bush told the book's author that he is convinced Clinton will be defeated by the Republican nominee.

Clinton, a U.S. senator from New York, has a wide lead in the polls over top rivals Sen. Barack Obama and former Sen. John Edwards. Many Republicans believe Clinton will be seen as a divisive figure and will serve to unite Republicans disenchanted by Bush's presidency.

"I think our candidate can beat her. But it's going to be a tough race," Bush said. "I will work to see to it that a Republican wins and therefore don't accept the premise that a Democrat will win. I truly think the Republicans will hold the White House."

Sammon wrote that other Bush officials were less certain about a favorable Republican outcome.

"It's going to be a very close election," former top Bush adviser Karl Rove said.

Vice President Dick Cheney said the election "could go either way."

"Right now, we're sort of in the area where we're pretty evenly balanced on both sides," he told Sammon.