Former US president Barack Obama has told allies in recent days that Joe Biden's path to victory has greatly diminished and he thinks the president needs to seriously consider the viability of his candidacy, the Washington Post reported on Thursday.
The Post cited multiple people briefed on Mr Obama's thinking.
Meanwhile, White House officials believe former House of Representatives speaker Nancy Pelosi backed representative Adam Schiff's call for Mr to step aside.
She has told Mr Biden he cannot win the November 5th election, a top White House source with direct knowledge of the matter said.
Mr Schiff said in a statement on Wednesday that he has "serious concerns" about whether Mr Biden can defeat Republican challenger Donald Trump, the first Democrat to come out after the Saturday assassination attempt against the former president.
Mr Biden's campaign had believed that the shooting, in which Mr Trump sustained a wound to the right ear, had tamped down calls for him to step aside in the 2024 race before Mr Schiff's statement.
"Nancy is all over this. She doesn't miss. Schiff wouldn't move without her approval," said the source, who spoke on condition of anonymity.
Ms Pelosi is "convinced public sentiment is against POTUS (president of the United States) and he can't change it," the source added.
Ms Pelosi's office and the White House did not respond to requests for comment.
Ms Pelosi, one of the most influential members of Mr Biden's party and a fixture in Washington for decades, likes to quote from a speech by former president Abraham Lincoln in leadership meetings, the source noted. In the speech, Lincoln said, "With public sentiment, nothing can fail; without it nothing can succeed."
"I don't think I would have said he's getting out of the race," before the public push from top Democratic leaders, the source said. "I hadn't seen a single crack from him but now who knows?"
"There is a path" to victory "but it's going to be hard. It will not be easy for Kamala," the source added, referring to vice president Kamala Harris, who potentially would replace Mr Biden as the Democratic presidential nominee.
Democrats are "doing this to ourselves. It is disappointing but we have to get through it, with or without a change" to the ticket, the source said, adding that there is "no other choice."
Some Democratic lawmakers in the House and Senate previously had called on Mr Biden to step aside in the race amid concerns about his fitness for the job at age 81. Mr Schiff and Ms Pelosi both represent California districts in the House.