According to The Wall Street Journal, Trump was leaning towards nominating Gary Cohn - who now serves as director of the National Economic Council - but soured after Cohn told Financial Times that Trump's response to the violence in Charlottesville wasn't good enough.
White House Chief of Staff John Kelly and Director of the White House National Economic Council Gary Cohn chat as they arrive with U.S. President Donald Trump (unseen) at White House after a trip to Springfield, Missouri, in Washington D.C., August 30, 2017.
But the president still has a long list of names for the position, including current Fed Chair Janet Yellen. A White House official added Cohn remained a key player in Trump's fight for tax reform. Trump had earlier said that Cohn was in the running for the job.
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But the critique to the FT caught Trump off guard, the Journal reported - and he now "visibly bristles" at the mention of Cohn.
Cohn, who is Jewish, told the Financial Times that the administration must do more to condemn neo-Nazis.
Trump's decision for Fed chair may come down to whether he would rather retain Yellen, despite her defense of banking regulation after the economic crisis, or choose someone new who may agree with him on the need for banking deregulation but also look for quicker interest-rate hikes.
Citing unnamed sources, the newspaper said Trump appears open to considering additional names for a pick he has promised to make by the end of the year.