While Senator Hillary Rodham Clinton and her advisers insist that she is determined to win the Democratic nomination, friends of the couple say that former President Bill Clinton, for one, has begun privately contemplating a different outcome for her: As Senator Barack Obama’s running mate.

The reports about Mr. Clinton’s musings surface as the Obama camp has quietly begun the process of searching for a partner on the Democratic ticket.

The prospect of an Obama-Clinton ticket has been fodder for political gossip for months, with some Democratic leaders pushing the idea as a way to unify the party. The Obama and Clinton campaigns have consistently shrugged off the idea, however, and Mrs. Clinton has been adamant that she is only interested in the presidency.

Yet anyone who knows the Clintons is well aware that, at times, they come to politics with different motivations. Both of them want to return to the White House; Mrs. Clinton, of New York, also enjoys being a senator, while Mr. Clinton, according to associates, sees the vice presidency as perhaps her best path to becoming president someday if she loses the nominating fight. And Mr. Clinton has his own ideas about his wife’s best interests  even if she sometimes does not share them.