"I'd love that," he said of the idea of the two grown men tussling as if they were high schoolers.
"Oh, some things in life you could really love doing," Trump added.
Trump attacked Biden as a "Mr. Tough Guy when he's standing behind a microphone by himself."
The vice president, for his part, has delivered some of the harshest and biting criticisms of Trump this election cycle.
While campaigning for Hillary Clinton last week in Wilkes Barre, Pennsylvania, the veep said he's always asked by reporters if he wished he were the one debating Trump.
"No," Biden responded. "I wish we were in high school. I could take him behind the gym. That's what I wish."
Trump lumped the tangential Biden attacks into a longer riff about why President Obama is campaigning and backing Hillary in lieu of Biden, who mulled a run late last year and decided against it. According to Trump, Obama is only backing Hillary — whom he did not endorse until late in the Democratic primary process — because he knew about the use of private email server.
Always one to wonder how the news cycle would play if he were the center of it, he theorized that if he said what Biden said the press would roast him as "violent."
Despite the throngs of fans gathered in the field before him, his barbs against the press earned fewer than expected cheers and jeers.