Biden, who will turn 75 on November 20, declined to seek the Democratic nomination for last year's presidential election in the wake of his son's death. He told NBC's "Today" show in an interview that he was not yet ready to enter a political contest.
"I honest to God haven't made up my mind about that," said Biden, who is promoting his memoir on Beau Biden, who died in 2015 from brain cancer. "Right now I want to focus on the book and I want to focus on winning the off-year elections.
"I'm not closing the door," said Biden, who added that he was in good health. But if he had to act right now, "I would say no because I am just working through a whole lot, I'm getting there and I want to focus on the book."
Biden served as vice president under Democratic former President Barack Obama for two terms but stood aside as the party nominated former Secretary of State Hillary Clinton, who lost to Trump last year. Biden had sought the Democratic presidential nomination for the 1988 and 2008 elections.
Biden, who represented Delaware in the Senate for 36 years, has long given voice to the working class. Although he campaigned for Clinton, he also has been critical after the Democrats' loss in 2016, which gave Republicans control of the White House in addition to their hold Congress.
Biden has criticised Trump in recent weeks, saying he "does not understand governance" and did not take a strong stand against white supremacists after a deadly rally in Charlottesville, Virginia, in August.