Some longtime aides and advisers to President Biden have become increasingly convinced that he will have to step aside from the campaign, and in recent days they have been trying to come up with ways to persuade him that he should, according to three people briefed on the matter.

A small group of Mr. Biden’s advisers in the administration and the campaign — at least two of whom have told allies that they do not believe he should keep trying to run for a second term — have said they would have to convince the president of several things.

They said they have to make the case to the president, who remains convinced of the strength of his campaign, that he cannot win against former President Donald J. Trump. They have to persuade him to believe that another candidate, like Vice President Kamala Harris, could beat Mr. Trump. And they have to assure Mr. Biden that, should he step aside, the process to choose another candidate would be orderly and not devolve into chaos in the Democratic Party.

Those discussions were recounted by three people familiar with them who, like others in this article, spoke on the condition of anonymity to discuss a sensitive situation. There is no indication that any of the discussions have reached Mr. Biden himself, one of the informed people said.

The White House denied the account. “Unequivocally, this is not true,” said Andrew Bates, a White House spokesman. “President Biden’s team is strongly behind him.”

The people who are closest to the president, a group that includes some of his longest-serving advisers and members of his family, remain adamant that Mr. Biden will stay in the race. A person familiar with the group dynamics said that such conversations are not happening in the group closest to Mr. Biden, that he is still committed to staying in the race, and that he still believes he is the best person to beat Mr. Trump.

The conversations have been happening outside that small orbit.

Among the biggest obstacles that those people see is convincing Mr. Biden that he cannot win. The president told confidants before his disastrous debate showing on June 27 that he believed he had a better chance of winning a second term than Ms. Harris had at winning, according to a person told of the matter. Two people close to the president said he remained convinced that he had a better chance of winning than she did.

The internal deliberations speak to the standoff between Mr. Biden and his party, in which the president has become increasingly entrenched in his conviction to run, and party leaders are publicly hinting that now may be the time for him to step aside.

Now, in the third week of the biggest political crisis to have faced his presidency, Mr. Biden remains convinced that he is the man to win. His view is increasingly at odds with the mood of voters and members of his own party.

A majority of Democrats feel that Mr. Biden should step aside, according to a Washington Post-ABC News-Ipsos poll published on Thursday. The poll also showed that the race remains close between Mr. Trump and Mr. Biden, but that Ms. Harris would fare slightly better if she were to replace him on the ballot. Mr. Biden and his advisers have long dismissed polling that shows concern over his age or ability to serve, and have been encouraged that polls continue to show a tight race between Mr. Biden and Mr. Trump two weeks after the debate.

A memo written by two top Biden campaign officials and distributed to staff on Thursday reaffirmed the view that Mr. Biden is still the best candidate to beat Mr. Trump.

“The movement we have seen, while real, is not a sea-change in the state of the race,” the memo, written by Jen O’Malley Dillon, the campaign chair, and Julie Chavez Rodriguez, said.