 The White House denies the account. The people who are the closest to the president, a group that includes some of his longest serving advisors 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 meet Mr. Trump. The conversations have been happening outside that small orbit.