An unnamed Republican strategist with insider knowledge on the White House told Politico report that President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE has privately expressed concern over former Vice President Joe Biden Joe BidenBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Democratic groups using Bloomberg money to launch M in Spanish language ads in Florida Harris faces pivotal moment with Supreme Court battle MORE's potential to beat him in the 2020 presidential election.

According to the report, Trump asked White House advisers last fall: "How are we gonna beat Biden?" Assured by his aides that Biden would not win the Democratic presidential primary, Trump reportedly continued, "but what if he does?"

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The anonymous strategist also told Politico that Trump's attacks on Biden in recent days illustrate Trump's purported fear of Biden as a candidate.

“The candidates he doesn’t talk about, it’s a signal that he doesn’t take them seriously,” they told the outlet.

Biden announced his 2020 presidential campaign Thursday morning, shortly after which Trump tweeted mocking him as "sleepy Joe."

“Welcome to the race Sleepy Joe. I only hope you have the intelligence, long in doubt, to wage a successful primary campaign,” Trump tweeted. "It will be nasty - you will be dealing with people who truly have some very sick & demented ideas. But if you make it, I will see you at the Starting Gate!"

The report and Trump's comment come after recent hypothetical polling, including a study released Wednesday, that show Biden leading Trump by 8 percentage points in a hypothetical 2020 general election matchup.

In July, Trump had called Biden his "dream opponent."

"I dream about Biden. That's a dream," Trump said. "Look, 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. I'd love to have it be Biden."

"I think I'd like to have any one of those people that we're talking about," he continued. "You know, there's probably – the group of seven or eight right now. I'd really like to – I'd like to run against any one of them, but Biden never by himself could never do anything."