Federal prosecutors in New York have sought documents from Franklin L. Haney, a top donor to President Trump, about his business dealings with Michael Cohen, according to people familiar with the matter.

Mr. Haney in early April hired Mr. Cohen, who at the time served as personal lawyer to the president, to help obtain funding for a nuclear-power project, including a $5 billion loan from the Department of Energy, the Journal reported last week, citing people familiar with the matter.

Mr....