Clinton's veep search is on

What's next for Clinton after clinching nomination?

Hillary Clinton is already searching for a vice presidential running mate and the presumptive Democratic presidential nominee says she's looking at "the most qualified people."

In an interview on CNN on Wednesday, Clinton was asked whether the country is ready for an all-female ticket.

Full interview: Clinton on challenges after making history

"I'm looking at the most qualified people and that includes women, of course, because I want to be sure that whoever I pick could be president immediately if something were to happen," Clinton told CNN. "That's the most important qualification."

But she also said she doesn't yet know whether or not she'll announce her running mate before the Democratic National Convention in Philadelphia this July.

"I'm not sure how long it's going to take to try and sort all this out. We'll have it done by the convention," she said. "I'm not going to speculate how much before the convention it'll be completed."

In 2008, then-Democratic presidential nominee Barack Obama announced Joe Biden would be his running mate in August, just ahead of the party's convention.

The CNN interview came a day after Clinton claimed victory in the Democratic primary race on Tuesday. Among the states that she won that day, she picked up California and New Jersey, which both had the most amount of delegates at stake. She actually clinched the nomination on Monday night after she secured enough superdelegates to reach the required threshold for the nomination.

Some of the potential running mates that have been floated are Sherrod Brown, Tim Kaine, Tom Perez, Elizabeth Warren and Julian Castro. Choosing Brown or Warren could be risky since they both represent states in the Senate that have GOP governors who would be able to appoint their successors. Warren has not yet endorsed Clinton.

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