While the nomination fight is still fluid, Mrs. Clinton is confident enough of victory that she has described a vision of a running mate and objectives for the search, according to campaign advisers and more than a dozen Democrats close to the campaign or the Clintons.

She does not have a front-runner in mind, they said, but she is intrigued by several contenders and scenarios.

Among the names under discussion by Mrs. Clinton, Mr. Clinton and campaign advisers: Senators Tim Kaine and Mark Warner, former governors from the key state of Virginia; Senator Sherrod Brown of Ohio, who represents both a more liberal wing of the party and a swing state; former Gov. Deval Patrick of Massachusetts, a prominent African-American Democrat; and Thomas E. Perez, President Obama’s labor secretary and a Hispanic civil rights lawyer.

But Mrs. Clinton is also open to a woman, campaign advisers said. One obvious possibility is Senator Elizabeth Warren of Massachusetts, who is hugely popular among progressive Democrats, though she has not been helpful to Mrs. Clinton’s campaign, declining to endorse the former secretary of state.