President Donald Trump is set to offer a position on the Federal Reserve to economic commentator and former campaign advisor Stephen Moore, CNBC has learned.

The president is waiting for Moore to get through the nominee clearance process.

Trump called Moore "a very respected" economist who he has known "for a long time — and have no doubt he will be an outstanding choice!"

Trump Moore tweet

In an interview earlier in the day, Moore said he had not been contacted at that point about an appointment.

"I could just say that I've been talking to some people about it, but I've not been formally offered a position," Moore told CNBC. "If I were offered it, I would do it."

Moore, 59, currently is a visiting fellow at the Heritage Foundation and former Wall Street Journal editorial board member and has been a Trump supporter since the 2016 election. In October 2018, he released the book with economist Art Laffer, "Trumponomics: Inside the America First Plan to Revive Our Economy."

Moore also has been a frequent Fed critic, saying the central bank's policies of keeping short-term rates near zero and buying bonds to stimulate growth were misguided and would spur inflation.

"If I were to do it I would certainly want to try to influence the Fed to a stable dollar and pro-growth monetary policy," he told CNBC.

Moore had been a contributor with CNN since 2017, but that relationship was terminated following Friday's news, according to a tweet by Brian Stelter, the network's chief media correspondent.

Reports had circulated in late-January that Trump was considering businessman and former presidential candidate Hermain Cain for a Fed governorship. Cain has previously served as chairman of the Kansas City Fed.

There currently are two governorship vacancies on the seven-member board.

—CNBC's Kayla Tausche contributed reporting.