Amy Klobuchar rumored possible pick for Clinton's vice president

The Fix on Hillary Clinton's vice presidential picks
The Fix on Hillary Clinton's vice presidential picks

As former Secretary of State Hillary Clinton's chances of securing the Democratic nomination increase, so has reporting and speculation about the people she might be considering as her running mate.

The New York Times confirmed this weekend that she's already begun the all-important vetting process.

Her campaign chairman, John Podesta, sparked rumors about who might be on that list last week when he confirmed there was "no question that there will be women on that list."

A new crop of names emerged over the weekend, including U.S. Sen. Amy Klobuchar of Minnesota.

Check out some of the other potential running mates Clinton's rumored to be considering:

Klobuchar is popular Democrat, described as "by far the best liked politician in the state" in a PPP survey released last year.

A Washington Post report suggested fellow U.S. Sen. Jeanne Shaheen of New Hampshire or former Homeland Security secretary and Arizona Gov. Janet Napolitano could also be on the list of women under consideration. Elizabeth Warren's name has been floated as well.

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But the latest speculation doesn't only include female politicians. U.S. Sen. Tim Kaine's name has also sprung up as a potential "short-list" candidate for Clinton. His counterpart from Virginia, Sen. Mark Warner, has been suggested as well.

U.S. Secretary of Housing and Urban Development Julián Castro continues to be considered the front-runner pick. As the Times report notes, "Several Democratic allies say that during the search, the campaign will have to reckon with Mrs. Clinton's high unfavorability numbers, which may create pressure to choose an inspiring figure like Julián Castro, the federal housing secretary, a rising star in the party."