Federal investigators in Manhattan have asked to interview Allen Weisselberg, the chief financial officer of the Trump Organization, as part of their investigation into President Trump’s former lawyer Michael D. Cohen, according to two people familiar with the matter.

It was not clear whether Mr. Weisselberg was issued a subpoena or was asked to answer questions voluntarily. Either way, the development suggests that federal prosecutors in the Southern District of New York are scrutinizing at least some financial dealings of the Trump family business, a line that the president has publicly warned the special counsel in the Russia investigation, Robert S. Mueller III, not to cross.

The New York prosecutors, who are operating on a separate track from Mr. Mueller’s team, are investigating Mr. Cohen on a number of fronts, including payments he arranged before the presidential election to women who had claimed that they had affairs with Mr. Trump. The prosecutors’ interest in Mr. Weisselberg was first reported by The Wall Street Journal.

The development set off alarm bells within the Trump Organization, an umbrella company for Mr. Trump’s holdings, because of the scope of Mr. Weisselberg’s responsibilities. He has handled its finances for decades, has been involved with the Trump Foundation, has managed the president’s private trust and has at times reviewed the Trump presidential campaign’s books.