"I have recommended Herman Cain", Trump told reporters in the Oval Office Thursday.
Cain, a former CEO of Godfather's Pizza, ran for the 2012 Republican presidential nomination but dropped out after allegations of sexual harassment and infidelity. In a 2012 Wall Street Journal column, Cain argued that the Fed's policies had manipulated the value of the dollar.
Mr Cain is well known for a series of gaffes and eyebrow-raising lines during his time as a contender for the Tea Party, a conservative movement within the Republican Party, during the party's primaries in 2011 and 2012.
Mr. Trump said officials are doing a background check, though he thinks Mr. Cain will be in "great shape".
Trump suggested those old claims would not disqualify Cain from a Fed post.
First of all, the gold standard is never going to happen.
At the time, Cain said the allegations were incorrect but acknowledged "he had made mistakes in my life", according to Bloomberg.
During his 2012 presidential campaign, Cain famously touted an economic plan, the "9-9-9 Plan", which would have replaced the US tax system with a flat 9 percent business, income and national sales tax.
Asked if he had any concerns, Trump said: "None whatsoever".
Trump has been highly critical of Powell, the person he picked to be Fed chairman after deciding that he would not renominate Janet Yellen.
Two previous and more orthodox Trump nominees, Nellie Liang and Marvin Goodfriend, were rejected by Congress a year ago.
President Donald Trump speaks in the Cabinet Room of the White House, April 4, 2019. She joined the Fed last year, taking over a term that will end next year.
"If Herman Cain were on the Fed, you'd know the interest rate would soon be 9-9-9".
Last month, Powell said the Fed would pause planned rate increases because the USA economy was slowing - and could continue to slow in part due to a prolonged Trump trade war with China.
Even with that change, Trump has kept up his attacks on the Fed.
"Despite the unnecessary and destructive actions taken by the Fed, the economy is looking very strong", Mr Trump tweeted.