In a letter sent to the president, the legislators tell Trump that "new leadership" is needed at the central bank to push the economy forward.
"As general mistrust of government and public institutions continues to rise, we believe that new leadership at the Federal Reserve will help restore its reputation as a forward-thinking monetary institution instead of a slow growth regulator," said the letter, authored by Reps. Warren Davidson, Ted Budd and Alex Mooney.
The letter comes as Trump nears the end of a selection process that has become convoluted and volatile in determining the next Fed chair. In recent days, Trump has indicated his decision likely is between Fed Governor Jerome "Jay" Powell and Stanford economist John Taylor.
However, he also has indicated that Yellen remains in the mix. Trump has expressed pleasure at how well the stock market has performed while Yellen has led the Fed and has been complimentary of her leadership.
The market has jumped since Trump won election last November, with the Dow industrials up more than 30 percent. The index is up about 45 percent since Yellen became Fed chair in February 2014.
However, the GOP members insist the Fed has overstepped its bounds elsewhere thanks to the "virtually unlimited regulatory authority" over the nation's banking system. They cite the Fed's "radical monetary experiment" that has included the central bank balance sheet swelling to $4.5 trillion thanks to three rounds of bond buying it engaged in to lower interest rates and stimulate the flow of money to riskier assets like stocks.
"These actions have blurred the line between fiscal and monetary policy almost beyond recognition, facilitating the Obama Administration's trail of reckless spending and doing so at the borrowed time of an unsustainable national debt on the backs of the American taxpayer," the letter stated.
Trump has said he expects to pick a new Fed chair before he leaves for his next foreign trip Nov. 3.