Joe Biden's dying son reportedly asked his father to promise that he'd run for president

When Beau Biden realized that he was going to die amid a battle with brain cancer earlier this year, he sat down with his father and asked him to make a promise: Run for president in 2016.

Vice President Joe Biden has been holding meetings at his Washington home to discuss challenging Hillary Clinton for the Democratic presidential nomination, The New York Times reported on Saturday, in a story that included the detail of Biden's conversation with his son.

"Beau was losing his nouns and the right side of his face was partially paralyzed. But he had a mission: He tried to make his father promise to run, arguing that the White House should not revert to the Clintons and that the country would be better off with Biden values," Times columnist Maureen Dowd wrote.

According to Dowd, Biden has been talking to friends, family and donors about the possibility of jumping in.

As the Washington Post notes, Beau Biden, the former attorney general of Delaware who died in May, had advocated for his father to run for president a third time despite opposition from other family members. The Wall Street Journal also reported in June that Beau encouraged his father to run.

The vice president's younger son, Hunter, also has pushed him to seek the presidency, the Times reported.

Biden himself hasn't hinted whether he's prepared to enter the race. On Saturday evening, The Washington Post suggested that the impetus to run may be primarily coming from longtime allies. Biden hasn't ruled out a run, and has said publicly he would make a decision at the end of the summer.

Despite being viewed more favorably than Clinton, according to one poll released earlier this week, Biden faces significant challenges if he does decide to jump in.

Clinton has already raised millions of dollars, established an official campaign infrastructure in several states, and garnered endorsements from dozens of prominent state and federal lawmakers. Though CNN reports that some Biden loyalists have held out to see if he will enter the race, others have already declared their support for Clinton.

If Biden does decide to enter the race, there is some infrastructure in place that could help him make up for lost ground. As the Chicago Sun Times reports, the "Draft Biden 2016" super PAC has been hiring campaign staffers in several early-voting states and collecting thousands of signatures to urge Biden to get into the race. A top former aide to Beau Biden has also joined the super PAC urging Joe Biden to run.

Biden has been slowly returning to a normal schedule following the death of his son two months ago. His public appearances have taken on a somewhat reflective tone.

At an event earlier this month in New York City celebrating the Supreme Court's gay marriage decision, Biden spoke about his long career as a progressive advocate in the Senate and about how his relationship with his father helped shape his views on same-sex marriage.

Dowd, who has often been critical of Clinton and her husband, former President Bill Clinton, said a campaign might be complicated for Biden because he has a good relationship with Hillary Clinton and respects the Democratic Party's desire to put a woman in the White House.

Biden has sought the Democratic presidential nomination twice before, in 1988 and 2008.

The White House had no immediate comment on Biden's plans, according to Reuters, and the Times quoted a spokeswoman for Biden as saying: "As the Biden family continues to go through this difficult time, the vice president is focused on his family and immersed in his work."