With her long Democratic primary fight now over, Clinton has privately signaled she is less concerned about choosing someone who fills a specific liberal or progressive void, rather than selecting a partner who is fully prepared for the job and has a strong camaraderie with her.
The list of serious vice presidential candidates is believed to be smaller rather than larger, with Democrats close to the campaign placing it at no more than five contenders. But several aides acknowledged they were not sure, considering the secrecy imposed on the process by Clinton.
Clinton has not yet conducted formal interviews, but has devoted hours studying the records and backgrounds of several Democrats on a list that includes Sen. Tim Kaine of Virginia, Sen. Elizabeth Warren of Massachusetts and Housing and Urban Development Secretary Julian Castro of Texas.
But those three should not be seen as absolute finalists, several Democrats said, only as active contenders. The roster also may include Labor Secretary Tom Perez, Sen. Sherrod Brown of Ohio and Rep. Xavier Beccera of California.
Asked about his prospects, Kaine smiled and winked Tuesday as he stepped into an elevator in the Capitol.
It does not include Sen. Bernie Sanders of Vermont, her primary rival who has yet to endorse her candidacy but has pledged to help defeat Donald Trump. He was not expecting to be considered, aides said, and her aides say he is not.
John Podesta, chairman of the Clinton campaign and a trusted confidante, is leading the effort, according to Democrats who spoke on the condition of anonymity because they are not authorized to speak about the highly-secretive process. Cheryl Mills, Clinton's longtime adviser and lawyer, is also helping Clinton with the decision.
Both were seen leaving Clinton's home in Washington on June 10, hours after the former secretary of state met with Warren. The topic of the meeting was not the vice presidency, aides said, but it was an opportunity for the two whose relationship has not always been warm to have a face-to-face conversation about the direction of the party.
As Clinton has repeatedly said in interviews, her top consideration is someone who would be able to step into the presidency should anything happen to her. And, by extension, someone who Republicans could not credibly cast as ill-prepared.
"I want to be sure that whoever I pick could be president immediately if something were to happen," Clinton told CNN earlier this month. "That's the most important qualification."
Another top consideration for Clinton and her aides, Democrats said, is finding someone she actually wants to work with, not necessarily someone who checks regional or specific electorate boxes. She, perhaps more than most presumptive nominees in recent history, knows the inner-workings of the West Wing intimately.
This could bode well for several Democrats, who aides say Clinton enjoyed campaigning with this year, including Kaine, Perez, Castro and Sen. Cory Booker of New Jersey.
For all the calculations about who would make a better running mate, the list of actual candidates is believed to be fairly small. Clinton is not expected to make a decision before Trump reveals his choice at the Republican convention, but aides say she is almost certain to have her decision made privately by then.
Each Democrat being considered offers a variety of pros and cons that Podesta, Mills and other aides are currently weighing. A veteran Washington lawyer, James Hamilton, is also overseeing the vetting of the candidates.
The real scrutiny, though, comes through the work of Democratic lawyers and researchers who are assigned specific candidates and are walled-off from others. They start by studying public records, searching for anything embarrassing, distracting or otherwise problematic.
One area of inquiry, for instance, is a batch of legal files in Richmond, Virginia, where death penalty cases of a young civil rights lawyer named Tim Kaine are being reviewed. Kaine was vetted by the Obama campaign eight years ago and people close to that process say nothing was discovered that would disqualify him.
Kaine, a former governor and chairman of the Democratic National Committee, is one of the few prospects with executive experience. He also speaks fluent Spanish, often conducting interviews on the campaign trail or on Capitol Hill in his second language. He is not a progressive firebrand, but that may be less of a demand than once thought during the heat of the Clinton-Sanders fight.
Castro is seen as young, vibrant and would further cement the Latino vote. But his experience is far less than anyone else on the list and some Democrats fear he could be cast as a lightweight.
Perez is seen as someone ready and willing to attack Trump and whose long history in labor politics could excite voters in labor strongholds like Ohio, Pennsylvania and Wisconsin. Yet he has spent most of his life as a political appointee, only successfully running for county council of Montgomery County, Maryland, in 2002.
While Warren is being actively considered, several Democrats close to both women are skeptical she will be selected. She has aggressively attacked Trump in recent weeks -- much to the delight of the Clinton campaign -- but the two do not have a personal relationship and Warren has, at times, been outspoken against some of the Clinton White House's policies.
Last week, Warren dropped by Clinton's headquarters and fired up the troops, leading one top Democrat to say: "Never say never. She's good."