The Axios news website based its reporting on comments from several top Democrats who said privately that rising intra-party pressures, including from leadership and close friends, "will persuade" him to step aside.
Concerns about the president's viability rapidly escalated after he badly faltered during a debate against now Republican nominee Donald Trump in June, raising further questions about the viability of re-electing a candidate who would be 86 years old at the end of a second term. Most polls show Biden now trailing significantly behind Trump in key battleground states with just four months until Election Day.
Biden, who is currently self-isolating following another COVID diagnosis, has not indicated publicly that he will heed the calls to end his campaign, despite senior Democratic donors and lawmakers adding their voice to the rising chorus demanding he step aside.
Representative Adam Schiff became the most high-profile member of Congress to do so on Wednesday when he said that Biden choosing to heed the calls would "secure his legacy of leadership by allowing us to defeat Donald Trump in the upcoming election."
Axios said Democrats are telling Biden behind the scenes similar things to what Schiff said publicly, namely that Trump could handily win in November, and would destroy Biden's legacy.
"His choice is to be one of history's heroes, or to be sure of the fact that there'll never be a Biden presidential library," one of Axios' anonymous sources said. "I pray that he does the right thing. He's headed that way."
A poll released earlier Thursday indicated that nearly four in five Democrats would support Vice President Kamala Harris replacing Biden if he bows to the mounting internal pressure.