Michael D. Cohen, President Trump’s former lawyer and fixer, met last month with federal prosecutors in Manhattan, offering information about possible irregularities within the president’s family business and about a donor to the inaugural committee, according to people familiar with the matter.

Mr. Cohen, who worked at the Trump Organization for a decade, spoke with the prosecutors about insurance claims the company had filed over the years, said the people, who did not elaborate on the nature of the possible irregularities.

While it was not clear whether the prosecutors found Mr. Cohen’s information credible and whether they intended to pursue it, the meeting suggests that they are interested in broader aspects of the Trump Organization, beyond their investigation into the company’s role in the hush money payments made before the 2016 election to women claiming to have had affairs with Mr. Trump. Mr. Cohen pleaded guilty last summer to arranging those payments.

The prosecutors also questioned Mr. Cohen about a donor to the president’s inaugural committee, Imaad Zuberi, a California venture capitalist and political fund-raiser, according to the people familiar with the matter, who were not authorized to discuss the confidential meeting. Around the time that Mr. Zuberi contributed $900,000 to the committee, he also tried to hire Mr. Cohen as a consultant and wrote him a substantial check, one of the people said.