Elizabeth Warren and Julian Castro on Clinton's VP Shortlist

U.S. Senators Elizabeth Warren of Massachusetts and Tim Kaine of Virginia, as well as rising star and U.S. Housing Secretary Julian Castro are on Democratic presidential candidate Hillary Clinton's shortlist of vice presidential picks, the Associated Press reported on Tuesday, citing Democratic sources.

Senator Warren has considered the idea of serving as Hillary Clinton's running mate, but sees obstacles to that choice as she prepares to endorse the presumptive Democratic presidential nominee, several people familiar with Warren's thinking told Reuters.

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Advisers to Warren – a fiery critic of Wall Street and popular figure among progressive Democrats – have been in close contact with Clinton's campaign team and the conversations have increased in frequency in recent weeks, the sources said. Warren has signaled to people close to her that she is intrigued by the possibility of being Clinton's No. 2.

Warren, 66, has been one of the Democrats' most outspoken critics of presumptive Republican presidential candidate Donald Trump, 69. Her priority is helping to defeat the presumptive Republican nominee in the Nov. 8 presidential election, the sources said.

Senator Tim Kaine of Virginia has also emerged as Clinton's potential running mate.

Clinton hasn't yet conducted formal interviews in the vetting process, which is closing in on its final weeks, according to CNN.

Clinton campaign chairman John Podesta is leading the VP effort, Democratic sources told CNN, and adviser Cheryl Mills is also helping the former secretary of state with the decision.