President Donald Trump speaks during a cabinet meeting in the Cabinet Room of the White House in Washington, DC on February 12, 2019. Mandel Ngan | AFP | Getty Images

President Donald Trump had a private meeting Monday with close advisors at the White House to discuss a wide range of topics, including the 2020 presidential election — and concerns about possibly facing former Vice President Joe Biden, CNBC has learned. At the meeting, the president seemed to indicate to some of his confidants that he is concerned about the prospect of facing Biden, according to one person who attended the gathering and declined to be named. In particular, Trump asked whether he should be concerned about Biden potentially capturing the Democratic nomination, according to people with direct knowledge of the matter. Trump had reportedly expressed concern during the 2018 midterm campaign about potentially facing Biden, although the president has said publicly that he isn't worried. The advisors told Trump that they're not convinced Biden would appeal to the Democratic Party's left wing or make it through a primary. They also told the president they believe Biden's opponents will say he's out of touch with the base of his own party. Biden, who leads in several primary polls of Democratic voters, has said that he's in the "final stages" of deciding whether he will run for president. When asked why the president spoke about Biden, one of the people with knowledge of the gathering told CNBC that the former vice president "is the least crazy out of all" the potential Democratic 2020 candidates. This person pointed to Biden's more moderate viewpoints compared with those of other Democrats running or considering entering the race. Another person familiar with the exchange brushed it off saying "no conclusions were reached," and that Trump is "gonna win in 2020 regardless."

Trump has ripped Biden for considering a 2020 run. In a recent Fox News interview, the president said he's not concerned about the Democratic field. "I'm not worried. So far I love the competition, I love what I see," Trump said in January. When asked at the time whom he would like to run against, Trump didn't commit to a particular candidate but went on to call Biden "weak" and claimed President Barack Obama "took him off the trash heap" when he chose him to be his vice president in 2008. A White House spokeswoman referred CNBC to the Trump campaign. Kayleigh McEnany, the Trump campaign's press secretary, did not return repeated requests for comment. Biden's spokesman declined to comment. The first contests of the primary are under a year away, while the first Democratic debates are slated for later this year. Early polls show Biden is the favorite among Democratic primary voters and may have an advantage over the president in a one-on-one election. In a 2018 POLITICO/Morning Consult poll, Biden led in a head-to-head matchup with Trump. Forty-four percent of voters said they would pick the former Delaware lawmaker, while Trump received support from 37 percent. The survey was of 1,993 registered voters from July 26 to July 30. Biden is leading in most of the national polls of the potential Democratic field, including a Morning Consult survey that shows him with 31 percent of early primary voters saying they would back him if he runs. Behind him are Sens. Bernie Sanders of Vermont, Kamala Harris of California and Elizabeth Warren of Massachusetts. The poll has a margin of error of plus or minus 1 percent.

The Biden dilemma

Political strategists from both sides of the aisle have mixed views about whether the president and his team should be worried about Biden entering the 2020 race. Democratic political strategist Mary-Anne Marsh questioned whether the third time will be the charm for the former vice president after he failed to make it through the primary the two other times he ran for the White House. "I think the biggest question is: Will Joe Biden be the better candidate when he runs this time compared to the two other times? He never made it to the general. So I think that's a big question," said Marsh, who worked on campaigns for Sens. John Kerry and Ted Kennedy. "Biden doesn't appeal to activists who dominated in 2016 and particularly the 2018 cycle. They are progressive, more women and people of color, and Biden's space are likely older, male and white." Biden, who represented Delaware in the U.S. Senate for more than three decades, ran for president in 1988 and 2008. A key Biden strength that could help him in the 2020 race is his skill on the stump. Democratic operatives involved with the 2018 midterms were grateful for Biden's assistance on the campaign trail as the party took back the majority in the House of Representatives.