Warren and Biden discussed economic policy during a meeting that lasted about two hours, a person familiar with the discussion told CNN, adding that the presidential campaign or Biden's future was not a particular focus of the discussion.
The meeting, confirmed by two people familiar with the session, is the biggest indication yet that Biden is feeling out influential Democrats before announcing his intentions.
Beloved by liberal Democrats, Warren decided to sit out a campaign of her own, but she has yet to formally endorse a candidate. In an interview on Friday, she told WBZ in Boston: "I don't think anyone has been anointed."
The vice president arrived in Washington shortly before lunchtime, even though his official schedule said he was planning to spend the weekend at his home in Delaware.
Kendra Barkoff, a Biden spokeswoman, declined to comment on the meeting. But an aide to Biden confirmed a meeting, telling CNN: "The vice president traveled last minute to Washington, D.C. for a private meeting and will be returning to Delaware."
Another source familiar with the meeting told CNN that Warren went to the meeting at Biden's request.
Biden is increasingly weighing whether to challenge Hillary Clinton and other Democratic candidates for the party's presidential nomination. A small team of advisers has spent weeks quietly putting together a campaign strategy and fundraising plan in case Biden decides to run. He had at least one meeting with them this week in Wilmington, one person familiar with the session told CNN.
He has told his associates he intends to make his decision in the next month, an announcement that could upend the fight for the Democratic presidential nomination.
With the Iowa caucuses and New Hampshire primary six months away, Biden is the leading figure Democrats believe they could turn to if they needed to find an alternative to Clinton, whose favorability ratings have taken a deep hit as her email use while secretary of state is drawing deeper controversy.
Biden, 72, has a large and loyal collection of friends and advisers from more than four decades in Washington. Yet even inside his sprawling constellation, affectionately known as "Biden World," deep divisions exist over the wisdom of him making another bid for the presidency.
Mapping out the steps
Earlier this week, Biden met with top advisers at his home in Delaware to further map out the steps to mounting a third presidential bid, though people familiar with the confab say the vice president is no closer to deciding on a run.
Biden met with his political team in Wilmington, where he spent the last week out of sight following a vacation in South Carolina. Longtime political allies Mike Donilon and former Sen. Ted Kaufman were among the operatives advising Biden on a run, a person familiar with the meeting said.
The factors Biden continues to mull include a timeline for getting in the race, and a fundraising plan that could help him launch a come-from-behind campaign against Clinton.
Like many Democrats, Biden and his team are carefully eyeing the continued questions about Clinton's email use at the State Department. Developments this week, including allegations that classified information may have passed through her private account, have led to new anxiety within the Democratic Party about the frontrunner's viability.
Those jitters haven't necessarily led to widespread calls for Biden to join the race; at the White House, there is some concern a Biden candidacy could end poorly and damage the vice president's reputation.
But with polls showing Clinton's trustworthiness slipping, some top Democrats are looking elsewhere.
"Frankly when it became clear that he was giving the race serious consideration, I just raised my hand," Steve Schale, who ran President Obama's 2008 and 2012 campaigns in Florida, told CNN on Wednesday. Last week Schale joined "Draft Biden," the independent group encouraging the vice president to run.
Draft Biden, which began earlier this year as a bare-bones effort to rally support behind Biden, has recently morphed into a full-fledged organizing campaign, including robust fundraising efforts, that could provide a framework for Biden should he jump into the race.
Costs of running
Biden's advisers have told the vice president he must decide by Oct. 1 -- roughly a week after his self-proclaimed "end-of-summer" deadline. A top Biden adviser told CNN this week the vice president is expected to wait at least until mid-September to announce a decision.
If Biden does mount a run for president, the cost of flying him from event to event on Air Force Two would come under scrutiny, as political travel for sitting presidents running for re-election has for decades.
Current regulations enacted during the last presidential election stipulate a candidate must reimburse the government for a pro-rated share of an equivalent-sized charter plane.
Biden often flies in a C-32, the military analogue to a Boeing 757. The cost to charter a 757 is between $12,000 and $15,000 per hour, according to charter companies.
That's far less than the actual costs to fly Air Force Two, which comes retrofitted with secure communication and navigation equipment, and costs north of $100,000 to operate per hour.
Travelers who must reimburse the government for political trips include the candidate and any staff traveling on behalf of his campaign. Other passengers, including security personnel, aren't required to reimburse the government for their portion of the trip.
The goal of the regulations: to ensure the costs of an office-holder's travel requirements neither hinder nor help a candidacy.
If he runs, Biden could combine campaign trips with official travel to mitigate the costs, which presidents have done for decades. The formula breaking down campaign and official costs, however, has been kept secret by White Houses going back to the 1970s.
The distinction between official and political travel has also been blurry in the past. Official travel requires the president or vice president to be advancing or explaining the work of the administration -- and as vice president, much of Biden's campaign pitch would entail doing just that.
Clinton has traveled using a mix of commercial and private air, none of which is nearly as large as a Boeing 757. The Gulfstream G500 she flew to Martha's Vineyard in on Saturday costs between $7,000-$8,000 to charter per hour.
But she or her campaign must foot the bill for the entire flight, not only a pro-rated portion of it, or a percentage split with official travel. Unlike Air Force Two, the government assumes none of the costs.
In her first quarterly FEC filing from July, Clinton's campaign reported spending almost $134,000 on a single private jet service, Executive Fliteways.
As a former first lady, Clinton travels with a Secret Service detail, though its footprint appears far smaller than Biden's. The Secret Service is not reimbursed for any costs associated with political travel.