Two sources said Trump remained upset with Cohn, a former Goldman Sachs president, for criticizing his response to the violence sparked by a white supremacist rally in Charlottesville, Virginia, last month.
A White House official said Cohn remained an essential player in Trump’s push for tax reform.
Another administration official said Trump was “considering several candidates” for the Fed.
Fed Chair Janet Yellen’s term expires in February.
Trump was widely criticized for blaming “many sides” for the Charlottesville violence, and Cohn stood with him during a news conference at Trump Tower in New York days after the rally when the president said there “very fine people” on both sides of the rally, which was attended by neo-Nazis.
Cohn looked visibly uncomfortable during those remarks and said later in an interview with the Financial Times that the administration had to do a better job of condemning hate groups.
Trump has said he would consider reappointing Yellen, who was nominated to lead the Fed by his Democratic predecessor, former President Barack Obama. Trump also has mused about backing Cohn.
Charlottesville helped changed that.
“He’s not getting it. Trump wants to fire him,” said one source with close ties to the White House who spoke on condition of anonymity.
“The president does not forget,” said another source close to Trump, referring to Cohn’s criticism.
Cohn is one of the main architects of the administration’s effort to reform the U.S. tax code and lower tax rates for individuals and corporations.
But the president did not single Cohn out for praise during a tax reform rollout speech last week in Missouri, sparking speculation that their relationship had cooled.
Cohn said in his interview with the Financial Times that he came under pressure to resign from the Trump administration.
Speculation in recent weeks that Cohn might be on the way out has rattled markets, but officials have insisted he planned on staying.
The Wall Street Journal reported that Trump and his advisers have discussed Stanford University economist John Taylor, former BB&T Bank Chief Executive John Allison, and former Fed governors Lawrence Lindsey and Kevin Warsh as possible appointees to the Fed’s Board of Governors. The Fed chair heads up the Board of Governors.
There are currently three vacant seats on the Fed Board of Governors, though Trump has nominated Utah investor Randal Quarles to fill one.
Trump’s choice for Fed chair may come down to whether he would rather keep 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 seek faster interest-rate hikes.
Most of the names who are thought to be in the mix for Fed chair are hawkish on interest rates, including Warsh, a former Wall Street banker who served as a Fed governor at the time of the financial crisis, and Taylor, author of a widely cited but only loosely followed mathematical rule for setting interest rates.
Allison has been an outspoken opponent of the Dodd-Frank banking regulations implemented in response to the financial crisis. Trump has criticized the regulations for slowing the economy.