"The shift in Mr. Cohn's prospects for the top Fed job arises largely from his criticism of Mr. Trump's response to the violence in Charlottesville, Va., the people familiar with the matter said", according the WSJ.
Federal Reserve Chair Janet Yellen's term expires in February 2018, leaving Trump with an increasingly narrow window to make his pick.
Mr Trump was widely criticised for blaming "many sides" for the Charlottesville violence, and Mr Cohn stood with him during a news conference in NY days after the rally when the President said there were "very fine people" on both sides of the rally, which was attended by neo-Nazis. Mr Trump had mused about backing Mr Cohn.
The White House didn't immediately return HuffPost's request for comment.
"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.
Cohn is viewed as a critical element of the administration's tax reform push both inside the administration and on Capitol Hill, where sources said Cohn has developed strong relationships with key players in the tax reform debate.
The president had previously said he was considering Cohn among other candidates.
Majority of the potential candidates who are in the mix for Fed chair are hawkish on interest rates, including Warsh, an ex- 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.