"He's a very terrific man, a terrific person".
The president last month offered a Fed position to another ally, conservative economist Stephen Moore. Moore's nomination has encountered criticism that he is unqualified and too politically focused for a Fed board seat.
Mr. Cain, the former CEO of Godfather Pizza, ran for the 2012 Republican presidential nomination.
Any Trump nominee must be confirmed by the Senate, and for what it's worth Utah's Republican Sen. "You want somebody on the Fed to be somebody who's very knowledgeable on economic issues".
Trump has announced plans to fill a second vacancy on the Fed board with another critic, Stephen Moore, who has echoed the president's own complaints that the Fed stifled economic growth by raising interest rates a year ago.
However, Larry Kudlow, head of the president's National Economic Council, told reporters Wednesday that Trump is "fully behind" Moore's nomination. Moore served as a campaign adviser to Trump in 2016 and helped formulate the president's signature tax cut plan. Moore now says that comment was written "in a time of anger".
Cain previously served as chair of the Federal Reserve Bank of Kansas City from 1995-1996. In a 2012 Wall Street Journal column, Cain argued that the Fed's policies had manipulated the value of the dollar.
First of all, the gold standard is never going to happen. The super PAC's website aims to "fight back" against the attack on America by those who wish to impeach Trump and his agenda. Mr. Trump also called Cain an "outstanding person".
Romney was referring to Cain's proposal from his 2012 presidential campaign that would erase all existing taxes and implement a 9 percent personal income tax, a 9 percent federal sales tax, and a 9 percent corporate tax.
Trump has repeatedly denounced the Fed leadership of Powell, whom he selected as chairman after deciding not to re-nominate Janet Yellen.
When Trump does eventually fill those two seats, six of the Board's seven members will be Trump appointees. Moore told the New York Times earlier this week that "it's full speed ahead" and said that the White House was "100%" behind him. Mr. Moore blames those increases for a drop in commodity prices at the end of past year.
Trump, however, has grown increasingly unhappy with Fed decisions under Powell's direction, especially after the stock market took a nosedive past year as the central bank was hiking rates four times.
Expectations are mounting among investors that the Fed could even cut its benchmark lending rates.