Later Friday, Trump responded to the report with a tweet criticizing the story and insisting that he supports Mnuchin.
"I am extremely happy and proud of the job being done" by Mnuchin, the president tweeted. "The FAKE NEWS likes to write stories to the contrary, quoting phony sources or jealous people, but they aren't true. They never like to ask me for a quote b/c it would kill their story."
The Journal did indeed reach out to the White House for comment.
In a statement to the Journal, White House spokeswoman Lindsay Walters said: "The president has long been clear about his views on the Fed. He has a good relationship with Secretary Mnuchin and is thankful for all the work he does on behalf of his administration and the American people."
Mnuchin reportedly made an aggressive push for Powell's nomination behind the scenes.
Trump picked Mnuchin in 2016 and has asked advisors whether he should have asked someone else to fill the job. In a White House with high turnover, Trump's complaints concerned some of Mnuchin's supporters, according to the Journal.
Trump criticized Mnuchin, pointing to recent stock market volatility, during a conversation with someone who praised his performance at the Treasury Department, the Journal reported, citing a person familiar with the matter.
"If he's so good, why is this happening?" Trump reportedly said.
In meetings with advisors, Trump has also expressed unhappiness with the Treasury Department's lack of support for tariffs against China, the newspaper said. Mnuchin, a former Goldman Sachs banker, is known for countering administration officials with more hawkish and protectionist views on China, such as trade advisor Peter Navarro.
Read the full report in The Wall Street Journal.
CNBC's Mike Calia contributed to this report.