Part of Trump's frustration with Powell has been the Fed chair's announcement last week of another hike in the benchmark interest rate, which caused markets to tumble.
The president lashed out at the Fed on Monday after administration officials spent the weekend trying to assure financial markets that Fed chairman Jerome Powell's job was safe.
"Secretary Mnuchin talks to bankers all the time, practically every day and you know, the markets clearly are focused on downside risk for next year and it's important to gather information from the normal sources and from informal sources and you know", Hassett said.
As markets struggled to gain a foothold Wednesday morning, the partial shutdown of the federal government entered its fifth day, with no immediate end in sight.
Investors have closely followed news that the president had privately discussed firing Powell.
While the comments were meant to be reassuring, they appear to have spooked investors instead.
His gradual interest rate hikes had reportedly created tension with the president.
US stock futures fell on Monday, giving up slim gains from earlier as volumes picked up, with investors digesting a slew of news from Washington over the weekend amid the benchmark S&P 500's worst December since the Great Depression.
The unusual and unprompted attempt at reassurance came after the Dow Jones Industrial Average posted its worst week since 2008 - the height of the financial crisis.
The Dow dropped by 2.9% and the S&P 500 fell 2.7%, the biggest drops ever for the two indexes on Christmas Eve. The Fed is like a powerful golfer who can't score because he has no touch - he can't putt!
The dollar index against a basket of six other major currencies dipped 0.46 percent to 96.511.
Many analysts blamed Monday's fall on some unexpected and apparently unprompted remarks from Secretary of the Treasury Steven Mnuchin about the health of the banking sector. He tweeted that he had spoken with the heads of the nation's six largest banks and was assured that they had sufficient lending capacity.
But investors said his move to convene a call with the President's Working Group on Financial Markets, known as the "Plunge Protection team", may have weighed on sentiment on Monday.
"I think there's an implication here for Nancy Pelosi's election for the speakership", Mulvaney said.
Trump has reportedly been frustrated with his Treasury secretary when the stock market wasn't doing great in recent weeks.
The stock market malaise comes with Mr Trump refusing to sign a budget bill to keep the government funded as he demands money for a US-Mexico border wall.