"We're in the final stages of that decision...But it would be the greatest honor of my life to be President of the United States," Biden said.
"But also...it's something that I have to make sure that I could run a first-rate effort to do this and make clear where I think the country should go and how to get there. That's the process going on right now. That's as straightforward as I can be. I have not made the final decision, but don't be surprised," Biden told presidential historian Jon Meachem.
One woman in the obviously friendly home-state crowd then prodded Biden with a shout of "Oh god, just say yes!"
Biden said he's been having family meetings recently, and some members of his family, including his wife Jill and son Hunter, want him to run.
"No man or woman has a right to run for high public office without it being a family decision. And from being pushed prodded by my son Hunter and my wife Jill and my daughter – we just had a family meeting with all the grandkids too – and there's a consensus that I should," he told the gathering. "The most important people in my life want me to run."
"The first hurdle for me was deciding whether or not I am comfortable taking the family through what would be a very, very, very difficult campaign," Biden, who ran unsuccessfully for the presidency in 2008 and later served for eight years as Vice President under President Barack Obama, said.
Other considerations Biden is mulling over in advance of a presidential bid include making sure his campaign has a social media strategy equipped for the digital age, a robust enough fundraising operation, and whether or not he can appeal to a wide enough range of voters to win both the Democratic primary and a general election.
"We are taking a hard look at whether or not this alleged appeal I have, how deep does it run? Is it real?" Biden said.
Were he to run, Biden said he would not "be a part of any super PAC," a significant step in field of candidates that have mostly shunned donations from corporations and other big money sources so far.
"I can die a happy man never having lived in the White House, but what I don't want to do is I don't want to take people's time, effort and commitment without there being a clear shot that I can be the nominee," he added.
Biden and Meachem were participating in the first event since the opening of the Biden School of Public Policy and Administration at the University of Delaware, a discussion on Meachem's recent book, "The Soul of America: The Battle for our Better Angels."
Biden also reflected on the trust and relationship he formed with Obama during the time they served in the White House together, saying that even when he disagreed with him, it was a relationship built on trust and understanding.
The former vice president also said he and Obama agreed not to comment on President Trump's administration during his first year in office, but that he felt a particular need to speak out after the racism and violence that erupted in Charlottesville, Virginia in August 2017.
"Barack and I agreed we were not going to comment on President Trump’s administration for a year to let him get set up…But when Charlottesville happened I couldn’t remain silent any longer," Biden said. "I was stunned."
Reflecting on what made past presidents successful, Biden focused on the concept of authenticity as the key component to a successful leader.
"In the time that I’ve observed...you are punished as a public official...if you turn out to be something different than what you advertise to be," Biden said.