WASHINGTON—President Donald Trump is unlikely to nominate Gary Cohn, his top economic adviser, as the next Federal Reserve chairman, according to people familiar with the president’s thinking, adding to the uncertainty over the U.S. central bank’s leadership and policies next year.

Mr. Trump told The Wall Street Journal in July that he was considering Mr. Cohn as a potential successor to Fed Chairwoman Janet Yellen, whose term as central bank chief expires in early February.

...