"I've told my folks that's the man," Trump told reporters in the Oval Office, adding that Cain is undergoing background checks before a nomination.
"He's a very terrific man, a terrific person," Trump said. "He's a friend of mine."
The choice of Cain would mark the second nomination to elevate a Trump ally with deep roots in conservative politics to the Fed's main policy-making body, a panel that the president has sharply criticized in recent months as insufficiently committed to low interest rates.
The president two weeks ago said he planned to nominate Stephen Moore for a separate vacancy on the board. 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. By design, the Fed is supposed to remain free of political taint in order to maintain the trust of financial markets and global policymakers.
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.
The selections of Cain and Moore would require Senate confirmation, and their potential nominations could face hurdles in the Senate. Sen. John Thune, the Republican whip, said lawmakers would want to question both men.
"They all have to go through the process and see whether or not they're a good fit — both in terms of qualifications and just the experience and everything else," Thune said. "You want somebody on the Fed to be somebody who's very knowledgeable on economic issues."
The seven-member Fed board, along with presidents of the Fed's regional banks, plays a critical role in the U.S. economy, holding meetings to debate and vote on interest rates that affect everything from currency values to mortgage rates to savings accounts to the health of the economy.
After Trump announced his intention to nominate Moore to the Fed board, published reports indicated that Moore had had a lien of more than $75,000 filed against him in January 2018 for unpaid taxes and that he has fallen behind on alimony and child support payments to his ex-wife.
Still, Larry Kudlow, Trump's top economic adviser, told reporters Wednesday that the president remains "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.
Like Trump, Moore has been sharply critical of the Fed, asserting in December that Chairman Jerome Powell should be fired for supporting a fourth Fed interest rate hike that month. Moore now says that comment was written "in a time of anger."
Cain met with Trump in January to discuss a possible nomination to the Fed board. But at the time, the White House said Trump was considering multiple candidates for the two vacancies on the Fed board.
Cain, who formerly served on the board of the Fed's Kansas City regional bank, has also criticized the central bank's policies. In a 2012 Wall Street Journal column, Cain argued that the Fed's policies had manipulated the value of the dollar. In the article, he advocated a return to the gold standard as a way to control inflation — a position taken by some other Fed critics but which most economists call unworkable.
In September, Cain co-founded a pro-Trump super political action committee, America Fighting Back PAC. It features a photo of the president on its website and says, "We must protect Donald Trump and his agenda from impeachment."
Cain dropped out of the race for the 2012 Republican presidential nomination after allegations that he had engaged in sexual harassment when he led the National Restaurant Association in the 1990s. An Atlanta woman also said she had conducted an extramarital affair with Cain for more than 13 years.
Cain called the allegations false but said he had "made mistakes in my life." Before leaving the race, Cain had put forward a "9-9-9" tax plan that called for replacing the current tax system with a flat 9 percent business and individual income tax, and a 9 percent sales tax.
Trump told reporters Thursday that he believed that after the background checks Cain would "be in great shape."
"I find Herman to be an outstanding person," he added.
Asked if he had any concerns, Trump said: "None whatsoever. He's a highly respected man. He's a friend of mine."
Trump has repeatedly denounced the Fed leadership of Powell, whom he selected as chairman after deciding not to re-nominate Janet Yellen. In addition to choosing Powell for the chairmanship, Trump has nominated all the current Fed board members with the exception of Lael Brainard, who was nominated by Barack Obama.
Trump's other nominees have held views more in line with traditional selections for the Fed board. The White House announced Thursday that Trump was nominating Michelle Bowman, a Kansas banking regulator, for a full 14-year term on the Fed. She joined the Fed last year, taking over a term that will end next year.
But Trump has grown increasingly unhappy with the Fed decisions under Powell, especially after the stock market tumbled last year as the central bank was hiking rates four times. Since January, the Fed has reversed course and now says it foresees no further rates hikes this year.
Even with that change, Trump has kept up his attacks on the Fed. Kudlow last week called for the Fed not only to pause rate hikes but to cut rates by a steep one-half percentage point and said the president believed that was the best course of action.
In a tweet Thursday, Trump said the economy was looking very strong "despite the unnecessary and destructive actions taken by the Fed."
AP White House reporter Darlene Superville and Chief Congressional Correspondent Lisa Mascaro contributed to this report.