A source in Biden's camp tells PEOPLE that he and his top advisors have, in the course of receiving condolences, heard from political friends and donors encouraging the Vice President to challenge former Secretary of State Hillary Clinton and the small handful of others currently seeking the 2016 Democratic presidential nomination.
"People have been reaching out to him," the source says. "He will decide by late summer, as he's always said."
Indeed, in February, ABC News reported that Biden told reporters in Iowa that running for president "is a family personal decision that I'm going to make sometime at the end of the summer."
What the press and public did not know at the time was that Biden's son, Beau, was privately battling brain cancer. He died at age 46 in May.
The Biden source on Sunday would not deny – nor confirm – a painfully, emotionally detailed account in Sunday's New York Times that Beau, before he passed, sat down with his dad and, "though Beau was losing his nouns and the right side of his face was partially paralyzed ... [he] tried to make his father promise to run."
"Dad, it's who you are," Times columnist Maureen Dowd quotes Beau's younger brother, Hunter as chiming in.
Biden, the former U.S. Senator from Delaware, ran for president twice before – in 1988 and in 2008, when he accepted then-Senator Barack Obama's vice presidential nomination.