But the Obama and Clinton campaigns have consistently shrugged off the idea, and Clinton has insisted that she will go all the way in her attempt to become the party's presidential nominee. Bill Clinton, according to his associates, sees the vice presidency as perhaps his wife's best path to becoming president someday if she loses the current nominating fight, though she does not share this view.
Friends of the former president say his musings have been more casual, and he believes an Obama-Clinton ticket could help unify the party. He thinks she has earned a meeting with Obama to discuss the possibility.
Clinton believes that his wife's victories in the key states of Ohio and Pennsylvania, and the 16 million votes cast for her candidacy make her the proper choice for Obama.
Clinton advisers were emphatic that neither Mr. Clinton nor anyone else in the campaign had given up on Mrs. Clinton's candidacy, and they emphasized that no efforts were being made to position Mrs. Clinton to be the running mate with the Illinois senator.
Meanwhile, Obama has asked a tight circle of advisers to set up a confidential search for prospective running mates, with a goal of having an early list of names to begin sifting through shortly after the final two primaries on June 3.
With the Democratic National Convention three months away, Obama is already about two months behind the period when preliminary vetting would normally have begun. The search will reportedly be guided by Jim Johnson, a longtime Democratic hand in Washington, though Obama declined reports that he had hired him. He just said that Johnson was a friend and that he would not be commenting on the issue of who would his vice-president, as he was yet to win the party's nomination for president.
Johnson, who is a vice chairman of the Obama campaign, led the vice presidential searches for Senator John Kerry, Democrat of Massachusetts, in 2004 and for Walter F. Mondale in 1984. In recent weeks, officials said, he started to compile information - largely biographical and political - for a list of potential running mates.