The surge has caught the attention of the president, who commented on Twitter that Mr Sanders is “looking very good against his opponents” and asked rhetorically “what does this all mean?”
“It means you’re going to lose,” Mr Sanders swiftly replied.
Recent polling shows the Vermont senator beating Mr Trump in a one-on-one fight by 2.6 per cent on average, according to RealClearPolitics’ analysis.
Last week, Mr Sanders secured a major boost to his campaign when he was shown to be leading in a widely-respected Des Moines Register/CNN poll for Iowa with 20 per cent of the vote, followed by Elizabeth Warren (17 per cent) and Pete Buttigieg (15 per cent).
He is also forecast to win in New Hampshire later in February, with close competition from Mr Buttigieg and former vice president Joe Biden.
Mr Trump’s decision to single-out Mr Sanders could indicate a change in tactics for the Republican president’s 2020 campaign, which has previously focused on attacking Mr Biden as his likely challenger in the election.
Despite Mr Biden performing poorly in Iowa and New Hampshire, he remains the frontrunner in the Democratic race due to his commanding leads in southern states, such as Texas and South Carolina, which vote later in the contest.
In recent weeks, Mr Sanders has intensified his criticism of the former vice president and argued that voters are not sufficiently energised by Mr Biden’s campaign to defeat Mr Trump.
In a leaked script for Sanders volunteers, campaigners have reportedly been told to push potential voters on “weaknesses” that Mr Trump could exploit against the former vice president, such as his support for free trade agreements and his vote for the Iraq War in 2003, according to Politico.
Mr Sanders’ campaign has also reportedly recommended volunteers argue that Mr Buttigieg cannot win over young people or African-American voters needed to defeat Mr Trump and suggest Ms Warren is the candidate for “highly-educated, more affluent people”.
Ms Warren, a personal friend with whom he has had an informal non-aggression pact, said she was "disappointed" by the report.
“Bernie knows me, and has known me for a long time, he knows who I am, where I come from, what I have worked on and fought for and the coalition and grassroots movement we’re trying to build", she said.
The senator’s campaign did not challenge the authenticity of the script but it has declined to comment to Politico on the leak.
In RealClearPolitics' polling average, Mr Biden is shown to be the strongest candidate against Mr Trump and defeats the current president by 4.5 per cent in a one-on-one contest.
Other candidates perform less favourably in a one-on-one against Mr Trump, with Ms Warren trailing the president by 0.2 per cent on average and Mr Buttigieg trailing by 1.2 per cent.