But that's if Biden chooses to run -- the decision is his. While he doesn't need the President's permission, of course, a potential presidential candidacy was among the topics of their lunch Monday at the White House. The President made clear he would not stand in his way or counsel him against a run, the senior Democrat said.
The Vice President's office downplayed the speculation about Biden's political future.
"Sources continue to speculate about something they know nothing about," Biden spokeswoman Kendra Barkoff said. "This lunch was a private meeting between two people -- the President and the Vice President."
The Vice President was expected to huddle at his home Monday night with Anita Dunn and Bob Bauer, the husband-and-wife team who have been at Obama's side for much of the last decade, two people familiar with the meeting told CNN. Steve Ricchetti, the Vice President's chief of staff, was also expected to attend.
"As a general rule, we are not going to confirm the Vice President's private meetings or provide a readout of them," an aide to the Vice President told CNN on Monday.
Dunn, a former White House communications director, and Bauer, a longtime lawyer to Obama, were among those invited to a meeting at the Naval Observatory in Washington. Ted Kaufman, a loyal Biden confidant who briefly occupied his Senate seat from Delaware, was also among those gathering to discuss how Biden could run, if he decides to do so.
Biden is leaning toward running, several people involved in discussions told CNN, but they stress that he has not yet firmly made up his mind.
The meeting on Monday night, along with his private session on Saturday with Sen. Elizabeth Warren, underscores the length he is going to explore a run.
While many top Democrats have already signed onto Hillary Clinton's candidacy, several former Obama advisers tell CNN they would work for Biden if he jumps into the race.
Dunn and Bauer would be a high-profile addition to any potential campaign, and could send a signal to other Democrats that they should join Biden's effort. It is not known if they would ultimately work for Biden if he does enter the race.
Bauer is one of the top Democratic election lawyers in Washington, who helped guide Obama's presidential campaign eight years ago. Dunn, a veteran of presidential campaigns, served as a communications director during Obama's first term. She was also an adviser to former Sen. Tom Daschle.
Key Democratic fundraisers have been invited to a meeting with Biden after Labor Day, a source close to Biden confirmed to CNN.
The Bauer-Dunn meeting is part of what CNN learned Monday will be an expanding schedule of Biden consultations with key Democrats, including state and national leaders, strategists and, significantly, Democratic donors and fundraisers.
Some of these conversations are being scheduled as political conversations and consultations. But Biden confidantes also noted he has several social events scheduled at the Vice President's residence over the next few weeks, and that an array of high-profile Democrats including Obama-Biden campaign fundraisers are among those on the invitation lists.
A Biden confidant who describes the Vice President as "more comfortable" with the idea of running said the sessions are among "several logical and necessary steps" the Vice President and his inner circle would be taking over the next several weeks.