President Trump said Thursday that he relishes the prospect of running against former Vice President Joseph R. Biden in the 2020 presidential election.

“I dream about Joe Biden,” Mr. Trump told CBS Evening News. “Joe Biden ran three times. He never got more than 1 percent, and President Obama took him out of the garbage heap, and everybody was shocked that he did.”

Mr. Biden has remained active on the political front, stumping with congressional candidates across the country and keeping open the possibility of running for the Democratic presidential nomination. The 75-year-old recently set a timetable for making a decision.

“I know I have to make up my mind, and I have to do it by January,” Mr. Biden said

Polls have shown Mr. Biden as an early front-runner in what is expected to be a big field of 2020 Democratic presidential contenders and likely to include, among others, Sens. Bernard Sanders of Vermont, Kirsten Gillibrand of New York and Elizabeth Warren of Massachusetts, as well as Sens. Cory Booker of New Jersey and Kamala Harris of California.

“I think I’d like to have any one of those people that we’re talking about.” Mr. Trump said. “You know, there’s probably — the group of seven or eight right now. … I’d like to run against any one of them, but Biden never by himself could never do anything.”

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