The official, speaking on condition of anonymity, said Bush is "very, very close" to settling on the former Defense Secretary but cautioned that the presumptive Republican nominee has not made a final decision.

The official made the disclosure after confirming that Cheney, a Texas businessman, switched his voter registration to Wyoming to avoid having two Texans on the ticket. "Today was the last day for him to register to vote in Wyoming so he could be a viable candidate for the governor's consideration," said the official.

Cheney's registration switch is designed to avoid conflict with language in the 12th Amendment of the Constitution that forbids the Electoral College voters in Texas from voting for both the president and vice president who are "inhabitants" of their state. Cheney is a former Wyoming lawmaker.

The official said Bush could still turn to other candidates, though the source would not say who remains in the running.

Other names that have figured prominently in the speculation including Govs. Frank Keating, Tom Ridge of Pennsylvania and George Pataki of New York; Rep. John Kasich of Ohio; and Sens. John McCain of Arizona, Chuck Hagel of Nebraska, and Fred Thompson and Bill Frist, both of Tennessee.

Bush said Friday he would decide on his running mate this weekend, pondering "long and hard" in the privacy of his ranch. "The days of speculation are over," Bush said, and aides indicated an announcement could come as early as Monday, a week before the opening of the Republican National Convention in Philadelphia.

Cheney would be a surprise pick. He suggested weeks ago that he would not be a candidate, after accepting the job of reviewing the backgrounds of potential candidates and helping Bush narrow his list.

His health would be a question. Cheney, 59, suffered three mild heart attacks by age 48, including one while campaigning for the Wyoming House seat in the primaries. He has undergone coronary bypass surgery.

In Congress, Cheney appealed to moderates, but racked up a conservative voting record and was a solid Ronald Reagan supporter. He served as Defense Secretary under Bush's father, former President Bush, from 1989-93 and successfully cut defense spending. He also was a key strategist in the Persian Gulf War.

He was mentioned as a possible vice presidential running mate for Bush in 1992.

Cheney emerged as the leading contender as the Bush campaign tried to dampen a lobbying effort on behalf of former primary rival John McCain.

McCain, who battled Bush unsuccessfully for the nomination -- and is anything but close to the Texas governor -- was injected forcefully into the late speculation. Several GOP sources said the head of the GOP House campaign committee, Rep. Tom Davis of Virginia, had solicited signatures on a letter to the Bush campaign urging consideration of the Arizona senator.

Bush gave no indication he would be influenced by the pressure, and observed he was certain that McCain would be a "loyal soldier for my candidacy."

McCain said, "I don't believe anything has changed" since a May meeting in which he told Bush he did not want to be considered.

McCain's political director, John Weaver, said he called Bush campaign manager Joe Allbaugh on Friday and said, "John's position has not changed since Pittsburgh and he doesn't want to be asked." In a subtle but important distinction, McCain has been more firm in the past, saying he doesn't want to be asked or serve as vice president.

Republican officials said Cheney had called several prominent Republicans -- McCain, Keating and Hagel among them -- to find out how they could be contacted in the next week or so.

About 60 Republicans -- more than one-fourth of the House GOP caucus -- signed the letter urging Bush to choose his one-time rival for the nomination, asserting that the only thing Democrat Al Gore fears "is George W. Bush calling John McCain."

The wording was disclosed by a Republican official who had the letter read to him. Circulated on the House floor for signatures, it was directed at Bush strategist Karl Rove and Cheney, the former defense secretary who has been heading Bush's running mate selection process.

The extraordinary public attempt to influence a nominee on the eve of his convention reflects the enormous stakes for November.

GOP leaders are struggling to hold their majority this fall in the face of a determined Democratic campaign for control. And they are eager for a national ticket that can appeal across party lines to the independents and Democratic voters who are likely to be pivotal in the battle for control of the House.

Rep. Lindsey Graham, a South Carolinian who backed McCain over Bush in that state's brutal GOP primary, spearheaded the signature-gathering effort, according to several GOP officials. Davis participated, and one Republican, Rep. Billy Tauzin of Louisiana, signed the letter Thursday night in the Virginian's presence at the campaign committee headquarters.

Bush, answering questions as he gave reporters a tour of his ranch, said when asked about the letter: "Until I've made up my mind, there will be a lot of people trying to give me advice. I appreciate the advice."

"I'm going to make up my mind over the weekend," he added.

Asked about McCain specifically, he said, "He'll be a loyal soldier for my candidacy. He is a man of duty and he loves his country." Bush has said loyalty is a trait he will demand in a nominee.

McCain had seemed to take himself out of the running in May, a move privately welcomed by Bush after their campaign struggle. But he and Ridge talked by telephone Tuesday, and McCain indicated that if Bush asked, "I would serve," according to GOP officials.

AP writers David Espo and Ron Fournier contributed to this story.