Speaking in Panama City Beach, Fla., Trump said that he hopes the Democrats quickly "pick somebody" to run against him.
"Let's start this thing," he said.
Trump appeared to doubt whether South Bend, Ind., Mayor Pete Buttigieg could handle complex negotiations with economic rival China.
"We have a young man, Buttigieg. ... He's got a great chance, doesn't he? He'll be great, representing us against President Xi of China -- that'll be great," Trump said.
"I want to be in that room, I want to watch that one," he said.
Trump added that China recently "broke" an economic agreement and that Vice Premier Liu He will be flying to Washington to negotiate a "deal" after tariffs were imposed on Beijing.
During the rally, Trump also expressed concern that several foreign leaders want Vice President Joe Biden to be president.
"Of course they do, so they can continue to rip off the United States," Trump said of the report. "I think if I heard that, I'd never vote for him."
"Sleepy Joe and Crazy Bernie [Sanders]," he said. "I'll take any of them."
Trump later asked the audience about former Rep. Beto O'Rourke, saying the Texas Dem's poll numbers appear to be "falling like a rock."
Conversely, Trump heaped praise on a number of Florida Republicans, including Gov. Ron DeSantis and Sens. Rick Scott and Marco Rubio.