"I have recommended Herman Cain," Trump told reporters in the Oval Office Thursday. "He's a very, terrific man, terrific person. He's a friend of mine. I have recommended him highly for the Fed. I told my folks that's the man. He's doing some pre-checking now and I would imagine he would be in great shape. I find Herman to be an outstanding person. A truly outstanding individual I think he would do very well there."
The former CEO of Godfather's Pizza, who turned the company into a top pizza franchise, is an ardent supporter of the president, launching a pro-Trump super PAC, America Fighting Back PAC in 2018. The PAC's website says it was founded by "a group of President Trump’s most committed supporters to fight this vile and uncalled for propaganda."
Axios reported earlier Thursday that Cain is being considered for the post.
Cain, who served on the board of the Kansas City Federal Reserve, opposed now-Sen. Mitt Romney, R-Utah, in the GOP presidential primary in 2012 but dropped out of the race after allegations emerged of sexual harassment and infidelity. Before his departure from the race, Cain was known for touting his "9-9-9" tax plan to reform the current tax system.
Since taking office, Trump has reshaped the seven-member board, nominating four members to its ranks, including Fed chairman Jerome Powell. Over the course of his presidency, Trump has sharply criticized Powell for raising interest rates to curb inflation, blaming the chair for hurting economic growth and suggesting his decisions undermine his administration's success.
"Had the Fed not mistakenly raised interest rates, especially since there is very little inflation, and had they not done the ridiculously timed quantitative tightening, the 3.0% GDP, & Stock Market, would have both been much higher & World Markets would be in a better place," the president tweeted last week.
Last month, Powell said the Fed would pause planned rate increases because the U.S. economy was slowing -- and could continue to slow in part due to a prolonged Trump trade war with China.
On Wednesday, White House economic advisor Larry Kudlow reinforced the president’ support for Moore, despite a New York Times report that he failed to fully pay taxes and alimony.
“I spoke to the president yesterday, he completely supports Steve. I certainly do. People are being awful hard on him,” Kudlow said. “This town is a toxic town in some respects. So we are fully behind him. He’s a smart guy. I think he’d be a breath of fresh air in the Fed, so far it’s all systems go.”
ABC News' Alexander Mallin, John Parkinson, Katherine Faulders and Amanda Maile contributed to this report.