By Michelle Conlin and Caren Bohan

NEW YORK/WASHINGTON (Reuters) - U.S. Senator Elizabeth 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.

While her thinking could evolve, Warren has concerns about joining a Clinton ticket, including the question of whether running two women would give the Democrats the best shot at defeating Republican Donald Trump, one source said.

Advisers to Warren, a fiery critic of Wall Street and a 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 but has not discussed the role with Clinton, 68, or anyone else from her campaign, the people said.

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

Warren is also committed to advancing her own political agenda, which they described as “more progressive” than Clinton’s more centrist positions. Warren fears that as vice president, or in a cabinet position, her voice could be less heard than it is in the U.S. Senate on her priority issues such as addressing income inequality, the sources said.

In the past, Warren has accused Clinton of abandoning her support for stronger bankruptcy legislation to try to appease Wall Street.

'GET READY DONALD'

An endorsement of Clinton could come within a week or two, one of the sources said. Clinton has been appealing for Democratic Party unity. On Twitter over the weekend, Warren echoed that call and emphasized the importance of the party coming together to beat Trump.

“Get ready, Donald,” Warren tweeted. “We're coming.”

Warren, who represents Massachusetts in the U.S. Senate, has stayed neutral in the Democratic primary race, notably remaining the only woman senator not throwing her support behind the first woman presidential nominee of a major U.S. political party.

Were she to join the Clinton ticket, she could help energize progressives and win over supporters of Clinton's rival Bernie Sanders, a democratic socialist U.S. senator from Vermont. Sanders' calls for reining in Wall Street and breaking up big banks dovetail with Warren's views.

An ongoing feud with Trump gained steam on social media with a series of posts in which she labeled the celebrity businessman racist, sexist and xenophobic and said she was going to fight to make sure his “toxic stew of hatred and insecurity never reaches the White House.”

Warren joined Clinton late last month in criticizing Trump for rooting for the 2008 financial crisis and delivered a 10-minute invective on the subject at an annual Washington gala two weeks ago.

“What kind of a man roots for people to get thrown out of their house? I’ll tell you exactly what kind of man does that,” Warren said. “It is a man who cares about no one but himself - a small insecure money-grubber who doesn’t care who gets hurt so long as he makes a profit off it.”

Trump has ridiculed Warren by calling her Pocahontas in a mocking reference to her having said in the past that she had Native American ancestry. Pocahontas was a famous Native American in early colonial Virginia.

Warren is due to speak to the American Constitution Society, a progressive legal group, on Thursday at a time when Democrats and some Republicans have criticized Trump's comments about Mexican-American Judge Gonzalo Curiel.

(Additional reporting by Megan Cassella and Amanda Becker in Washington; Editing by Amran Abocar, Kevin Krolicki and Howard Goller)