Biden, who served as a senator before becoming a vice-president, is one of many Democrats seeking a presidential election in 2020. Without being officially appointed, Biden spoke of his qualifications.
"I think I'm the most qualified person in the country to be president," Biden said during a reading tour at the University of Montana in December. "The problems we face as a country today are those in my own driving room, on which I have worked all my life."
Trump ridiculed Biden as a "1%" in an interview with Pirro.
"He's gone two or three times and has not received more than 1%," said Trump. "Then Obama came and took him out of the trash and became vice president."
"He's weak, so we'll see what happens to him," Trump said.
Trump also weighed on other potential rivals during the 2020 presidential race.
Senator Elizabeth Warren, Massachusetts Senator Tulsi Gabard, and former Housing and Urban Development Secretary Julian Castro recently announced offers.
"I'm not worried," said Trump. "Until now, I like competition, I like what I see."
Many other well-known Democrats have not announced their intentions to run, but have taken steps to signal that the announcement may soon come, including by strengthening their staff and making trips to key states and large groups.
Senators: Kamala Harris, Kirsten Gillibrand, Cory Booker and Bernie Sanders. Former New York Mayor Michael Bloomberg. And former Rep. Beto Aurecch among those who hinted that they escaped.
The Californian billionaire and frequent critic of Trump, Tom Steyr, announced earlier this year that he would seek the office.