Both Mr. Rechnitz and Mr. Reichberg served on a committee that planned Mr. de Blasio’s 2014 inaugural celebration. Mr. Rechnitz owns a real estate development and management firm that controls several buildings in Brooklyn and Manhattan. Mr. Reichberg operates a consulting company, but the precise nature of its business is unclear.

Two of the people briefed on the matter suggested that investigators were trying to determine whether Mr. Rechnitz and Mr. Reichberg benefited from some type of favorable municipal action, or the promise of some action, in exchange for their donations, their fund-raising or some other gesture. But the precise allegations under scrutiny by federal prosecutors in Manhattan and agents of the Federal Bureau of Investigation are unclear. The two people, like others interviewed for this article, spoke on the condition of anonymity because they were not authorized to talk about the case publicly.

Neither man has been charged with a crime.

To date, there has been no suggestion that Mr. de Blasio was involved in any improprieties, and it remains unclear whether the prosecutors and F.B.I. agents working on the case have developed evidence, conclusive or otherwise, of the kind of quid pro quo necessary to prove most corruption crimes in federal court. Speaking to reporters on Sunday, Mr. de Blasio said no one in his administration had been contacted by investigators, and he described his relationship with the two businessmen as cursory.

A lawyer for Mr. Rechnitz, Marc S. Harris, said last week that his client had broken no laws and that he had not been notified that he was the subject of any inquiry. Mr. Reichberg could not be reached for comment. A lawyer who was said to represent Mr. Reichberg said last week that she does not comment on who she does or does not represent.

Both the United States attorney’s office in Manhattan and the F.B.I., which are conducting the investigation, declined to comment.