Dowd wrote on Saturday that Joe's late son Beau Biden was pushing his father to run for the Democratic nomination before passing away from brain cancer in May.
"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," Dowd wrote in her column of Beau encouraging his dad.
She also reported that Joe, 72, has been holding meetings at his home in Washington to explore the idea of challenging front runner Hillary Clinton.
"Joe Biden knows what Beau wants. Now he just has to decide if it's who he is," wrote Dowd.
Joe has yet to publicly comment on his intentions to run for election in 2016.
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Beau, 46, was laid to rest on June 5 in the family's hometown of Wilmington, Delaware.
The Biden family is no stranger to tragedy – Joe's first wife and baby daughter were killed in a car crash in 1972. Beau, who was 4 at the time, and his brother Hunter, then 3, were hospitalized at length after the accident.
Beau, who joined the military in 2003 and was deployed to Iraq in 2008, served as the 44th Attorney General of Delaware from January 2007 to Jan. 6, 2015.
Joe paid a surprise visit to the Emanuel AME Church in Charleston, South Carolina, in June to join the morning services at the historic house of worship where nine people were killed.
"I wish I could say something that would ease the pains of the families and of the church," Joe said. "But I know from experience, and I was reminded of it again 29 days ago, that no words can mend a broken heart."