Vice President Joe Biden and his associates have begun to actively explore a possible presidential campaign, an entry that would upend the Democratic field and deliver a direct threat to Hillary Rodham Clinton, say several people who have spoken to Biden or his closest advisers.

Biden’s advisers have started to reach out to Democratic leaders and donors who have not yet committed to Clinton or who have grown concerned about what they see as her increasingly visible vulnerabilities as a candidate.

On Saturday, Maureen Dowd, a New York Times columnist, reported that Biden had been holding meetings at his residence, “talking to friends, family and donors about jumping in” to challenge Clinton in Iowa and New Hampshire, the first two nominating states.

One longtime Biden supporter said the vice president has been deeply moved by his son’s desire for him to run.

“He was so close to Beau and it was so heartbreaking that, frankly, I thought initially he wouldn’t have the heart,” Michael Thornton, a Boston lawyer who is a Biden supporter, said in an interview. “But I’ve had indications that maybe he does want to — and ‘that’s what Beau would have wanted me to do.’ ”

New York Times