Sources close to the White House have signaled in the last week that Cohn appears unlikely to be removed due to his critical role on tax reform and Trump has been warned against ousting Cohn for that same reason.
Cohn's public criticism of the President's reaction to the events in Charlottesville is reportedly why Trump has soured at the idea of appointing his top economic adviser.More news: European Union court orders Slovakia and Hungary to accept asylum-seekers
The Journal reported Cohn told associates he was disgusted by Trump's performance immediately after the president's August 15 news conference about the Charlottesville events.More news: Prince William, Kate expecting third child, Kensington Palace says
Trump has said he would consider reappointing Yellen, who was nominated to lead the Fed by his Democratic predecessor, former President Barack Obama.
A White House official said Cohn remained an essential player in Trump's push for tax reform.More news: Japan confirms North Korea has conducted sixth nuclear test
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.