The announcement comes weeks after Trump floated another nominee to fill an open seat on the Fed board: Stephen Moore, a former campaign adviser and distinguished fellow at the conservative Heritage Foundation. Moore's nomination has ignited criticism that he is unqualified and too politically minded to serve on the board of the world's most influential central bank.
Cain met with Trump in January to discuss a possible nomination to the Fed board but at the time the White House said that Trump was looking at multiple candidates for the two Fed openings. The role requires Senate confirmation and any vetting process is likely to resurface allegations Cain faced over sexual harassment and infidelity that ended his bid for the Republican nomination.
In a 2012 Wall Street Journal column, Cain said that the Fed's policies manipulated the value of the dollar.
Neither Moore nor Cain has officially been nominated for the Federal Reserve Board.
Trump suggested those old claims would not disqualify Cain from a Fed post. An Atlanta woman also said she had conducted an extramarital affair with Cain for more than 13 years.
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 been highly critical of Powell, the person he picked to be Fed chairman after deciding that he would not renominate Janet Yellen. He did not respond to a request for comment.
This year the Fed has put rate hikes on hold, citing a slowing economy and risks from overseas.
While the links between Fed interest rate policy policy and the money supply are complex and much-argued, the general theory Moore is working under is that lower interest rates will help goose employment and asset values in the short term, which is good for Trump.
Expectations are mounting among investors that the Fed could even cut its benchmark lending rates.