Clinton's remarks came in response to a question from Democratic Rep. Nydia Velazquez, who said she believed the best way for Obama to win key voting blocs, including Hispanics, would be for him to choose Clinton as his running mate.
"I am open to it," Clinton replied, if it would help the party's prospects in November.
Clinton also told colleagues the delegate math was not there for her to overtake Obama, but that she wanted to take time to determine how to leave the race in a way that would best help Democrats.
"I deserve some time to get this right," she said, even as the other lawmakers forcefully argued for her to press Obama to choose her as his running mate.
Joseph Crowley, a Queens Democrat who participated in the call, said her answer "left open the possibility that she would do anything that she can to contribute toward a Democratic victory in November. There was no hedging on that. Whatever she can do to contribute, she was willing to do."
Another person on the call, Rep. Jose Serrano of New York City, said her answer was "just what I was hoping to hear. ... Of course she was interested in being president, but she's just as interested in making sure Democrats get elected in November."
Rep. Charles Rangel, a devoted booster of Clinton who helped pave the way for her successful Senate campaign, said he spoke to her Tuesday and got much the same answer.
"She's run a great campaign and even though she'll be a great senator, she has a lot of followers that obviously Obama doesn't have, and clearly the numbers are against her and so I think they bring all parts of the Democratic Party together and then some," Rangel said.
Aides to the Illinois senator said he and Clinton had not spoken about the prospects of her joining the ticket.
Obama effectively sewed up the 2,118 delegates needed to win the nomination Tuesday, based on a tally of pledged delegates, superdelegates who have declared their preference, and another 18 superdelegates who have confirmed their intentions to The Associated Press. It also included five delegates Obama was guaranteed as long as he gained 15 percent of the vote in South Dakota and Montana later in the day.
Word of Clinton's vice presidential musings came as she prepared to deliver a televised address to supporters on the final night of the epic primary season. She was working out final details of the speech at her Chappaqua, N.Y., home with her husband, former President Bill Clinton, their daughter Chelsea, and close aides.
Earlier, on NBC's "Today Show," Clinton campaign chairman Terry McAuliffe said that once Obama gets the majority of convention delegates, "I think Hillary Clinton will congratulate him and call him the nominee."
Clinton will pledge to continue to speak out on issues like health care. But for all intents and purposes, two senior officials said, her campaign is over.
Most campaign staff will be let go and will be paid through June 15, said the officials who spoke on condition of anonymity because they were not authorized to divulge her plans.
The advisers said Clinton has made a strategic decision to not formally end her campaign, giving her leverage to negotiate with Obama on various matters including a possible vice presidential nomination for her. She also wants to press him on issues he should focus on in the fall, such as health care.
Universal health care, Clinton's signature issue as first lady in the 1990s, was a point of dispute between Obama and the New York senator during their epic nomination fight.
In a formal statement, the campaign made clear the limits of how far she would go in Tuesday night's speech. "Senator Clinton will not concede the nomination," the statement said.
Clinton field hands who worked in key battlegrounds said they were told to stand down, without pay, and await instructions. Speaking not for attribution because they didn't want to jeopardize their jobs searches, many said they were peddling resumes, returning to their hometowns or seeking out former employers.
Clinton officials have said they would not contest the seating of Michigan delegates at the convention in Denver this August. The campaign was angry this past weekend when a Democratic National Committee panel awarded Obama delegates it thought Clinton deserved.