Donald Trump has told aides of his fears that Joe Biden could beat him in next year’s presidential election.

Mr Trump has hit out at the former vice president via Twitter in recent days, labelling Mr Biden “sleepy Joe” and questioning his intelligence – but the intervention belies a belief that Mr Biden is a serious rival.

“The candidates he doesn’t talk about, it’s a signal that he doesn’t take them seriously,” a Republican strategist close to the Trump campaign told Politico.

Mr Trump and Mr Biden have regularly traded barbs during the president’s term. In March 2018 Mr Biden said he would have “beat the hell” out of Mr Trump if the pair were in high school over his remarks about women, while Mr Trump has repeatedly hit out at Mr Biden’s previous presidential runs at rallies.

Mr Biden has also repeatedly admonished Mr Trump for the direction he is taking America.

The Democrat challengers to Trump in 2020 Show all 25 1 /25 The Democrat challengers to Trump in 2020 The Democrat challengers to Trump in 2020 Bernie Sanders The Vermont senator has launched a second bid for president after losing out to Hilary Clinton in the 2016 Democratic primaries. He is running on a similar platform of democratic socialist reform Getty The Democrat challengers to Trump in 2020 Joe Biden The former vice president recently faced scrutiny for inappropriate touching of women, but was thought to deal with the criticism well and has since maintained a front runner status in national polling EPA The Democrat challengers to Trump in 2020 Elizabeth Warren The Massachusetts senator is a progressive Democrat, and a major supporter of regulating Wall Street Reuters The Democrat challengers to Trump in 2020 Amy Klobuchar Klobuchar is a Minnesota senator who earned praise for her contribution to the Brett Kavanaugh hearings Getty The Democrat challengers to Trump in 2020 Michael Bloomberg Michael Bloomberg, a late addition to the 2020 race, announced his candidacy after months of speculation in November. He has launched a massive ad-buying campaign and issued an apology for the controversial "stop and frisk" programme that adversely impacted minority communities in New York City when he was mayor Getty Images The Democrat challengers to Trump in 2020 Tulsi Gabbard The Hawaii congresswoman announced her candidacy in January, but has faced tough questions on her past comments on LGBT+ rights and her stance on Syrian President Bashar al-Assad Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Pete Buttigieg The centrist Indiana mayor and war veteran would be the first openly LGBT+ president in American history Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Deval Patrick The former Massachusetts governor launched a late 2020 candidacy and received very little reception. With just a few short months until the first voters flock to the polls, the former governor is running as a centrist and believes he can unite the party's various voting blocs AFP/Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Beto O'Rourke The former Texas congressman formally launched his bid for the presidency in March. He ran on a progressive platform, stating that the US is driven by "gross differences in opportunity and outcome" AP The Democrat challengers to Trump in 2020 DROPPED OUT: Kamala Harris The former California attorney general was introduced to the national stage during Jeff Sessions’ testimony. She has endorsed Medicare-for-all and proposed a major tax-credit for the middle class AFP/Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Bill De Blasio The New York mayor announced his bid on 16 May 2019. He emerged in 2013 as a leading voice in the left wing of his party but struggled to build a national profile and has suffered a number of political setbacks in his time as mayor AFP/Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Steve Bullock The Montana governor announced his bid on 14 May. He stated "We need to defeat Donald Trump in 2020 and defeat the corrupt system that lets campaign money drown out the people's voice, so we can finally make good on the promise of a fair shot for everyone." He also highlighted the fact that he won the governor's seat in a red [Republican] state Reuters The Democrat challengers to Trump in 2020 DROPPED OUT: Cory Booker The New Jersey Senator has focused on restoring kindness and civility in American politics throughout his campaign, though he has failed to secure the same level of support and fundraising as several other senators running for the White House in 2020 Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Wayne Messam Mayor of the city of Miramar in the Miami metropolitan area, Wayne Messam said he intended to run on a progressive platform against the "broken" federal government. He favours gun regulations and was a signatory to a letter from some 400 mayors condemning President Trump's withdrawal from the Paris Climate Accord Vice News The Democrat challengers to Trump in 2020 DROPPED OUT: Kirsten Gillibrand The New York Senator formally announced her presidential bid in January, saying that “healthcare should be a right, not a privilege” Getty The Democrat challengers to Trump in 2020 DROPPED OUT: John Delaney The Maryland congressman was the first to launch his bid for presidency, making the announcement in 2017 AP The Democrat challengers to Trump in 2020 DROPPED OUT: Andrew Yang The entrepreneur announced his presidential candidacy by pledging that he would introduce a universal basic income of $1,000 a month to every American over the age of 18 Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Julian Castro The former San Antonio mayor announced his candidacy in January and said that his running has a “special meaning” for the Latino community in the US Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Marianne Williamson The author and spiritual adviser has announced her intention to run for president. She had previously run for congress as an independent in 2014 but was unsuccessful Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Eric Swalwell One of the younger candidates, Swalwell has served on multiple committees in the House of Representatives. He intended to make gun control central to his campaign but dropped out after his team said it was clear there was no path to victory Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Seth Moulton A Massachusetts congressman, Moulton is a former US soldier who is best known for trying to stop Nancy Pelosi from becoming speaker of the house. He dropped out of the race after not polling well in key states Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Jay Inslee Inslee has been governor of Washington since 2013. His bid was centred around climate change AFP/Getty The Democrat challengers to Trump in 2020 DROPPED OUT: John Hickenlooper The former governor of Colorado aimed to sell himself as an effective leader who was open to compromise, but failed to make a splash on the national stage Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Tim Ryan Ohio representative Tim Ryan ran on a campaign that hinged on his working class roots, though his messaging did not appear to resonate with voters Getty The Democrat challengers to Trump in 2020 DROPPED OUT: Tom Steyer Democratic presidential hopeful billionaire and philanthropist Tom Steyer is a longtime Democratic donor AFP/Getty

As early as last Autumn, Mr Trump was discussing with his aides about the threat posed by the former vice president.

“How are we gonna beat Biden?” he would ask, according to the Republican strategist. After being assured that Mr Biden would never make it out of a tough Democratic primary, Mr Trump pushed back: “But what if he does?” Mr Biden eventually announced his candidacy on Thursday.

In July 2018 Mr Trump called Mr Biden his “dream opponent” during an interview with CBS News. “Look, Joe Biden ran three times. He never got more than 1 per cent and President Obama took him out of the garbage heap, and everybody was shocked that he did,” Mr Trump said. However, such confident public statements often contradict the descriptions of the presidents demeanour during private meetings.

Early, hypothetical polling of a potential Trump-Biden match-up in the 2020 election has Mr Biden leading the president by eight percentage points. The Morning Consult/Politico poll of nearly 2,000 voters, released on Wednesday, shows Mr Biden supported by 42 per cent of registered voters with Mr Trump backed by 34 per cent of voters.

Mr Trump’s apparent fears about Mr Biden’s candidacy could be related to the fact that he has more in common with the former vice president than the rest of the Democrat field. Both are in their 70s and have been able to win over blue-collar, high-school educated voters. Indeed in states like Michigan and Pennsylvania that could prove crucial, it is thought Mr Biden will be able to compete closely with Mr Trump.

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Both also are prone to making remarks and gaffes that can lead to ridicule, and both speak more often to the press and in public than their teams may be comfortable with.