This is largely because of Cohn's public rebuke of Trump's initial response to the deadly white-supremacist riots in Charlottesville last month, the report said. A White House official added Cohn remained a key player in Trump's fight for tax reform.
After a neo-Nazi murdered counter-protestor Heather Hayer by plowing his auto into a crowd of people, Trump condemned violence "on many sides" and noted a few days later there were "very fine people on both sides".
Hillary Clinton Was "Deeply Unsure" Her Marriage to Bill Clinton Would Survive
The former Secretary of State added that she fears the Trump Administration will make it more hard for women to succeed. Sanders told The Hill : "My response is that right now it's appropriate to look forward and not backward".
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.
The president had previously said he was considering Cohn among other candidates.
A person close to Trump said that he wasn't expecting Cohn's comments, while another source told TheWSJ that Trump seems annoyed when Cohn's name is mentioned.
Cohn is one of the main architects of the administration's effort to reform the USA tax code and lower tax rates for individuals and corporations. But the President did not single Mr Cohn out for praise during a tax reform roll-out speech last week in Missouri, sparking speculation that their relationship had cooled.