One of the people insisted that Mr. Barr had been weighing his departure since before last week and that Mr. Trump had not affected the attorney general’s thinking. Another said Mr. Barr had concluded that he had completed the work that he set out to accomplish at the Justice Department.

But the president’s public complaints about the election, including a baseless allegation earlier last week that federal law enforcement had rigged the election against him, are certain to cast a cloud over any early departure by Mr. Barr. By leaving early, Mr. Barr could avoid a confrontation with the president over his refusal to advance Mr. Trump’s efforts to rewrite the election results.

Mr. Barr’s departure would also deprive the president of a cabinet officer who has wielded the power of the Justice Department more deeply in service of a president’s political agenda than any attorney general in a half-century. Conversely, it would please some Trump allies, who have called for Mr. Barr to step down over his refusal to wade further into Mr. Trump’s efforts to overturn the election outcome.