Eleven of its 17 policymakers forecast no rate hikes this year, and Fed Chairman Jerome Powell cited low inflation, a slowing global economy and risks like US trade tensions with China for the need to remain patient "for some time".
Meanwhile, the Fed announced this week it will hold interest rates steady, indicating no more hikes set to come down the pike this year.
Trump in his first two years in office has been able to reshape the central bank.
Trump remarked to Kudlow that he should have appointed Moore to be Fed chairman, the people said and directed Kudlow to call Moore and gauge his interest in a board seat.
Trump was so incensed by the Fed's policies he is said to have sought advice late a year ago on whether he could fire its chairman, Jerome Powell.
Powell said in a news conference that GDP growth is slower than expected and the Fed now projects 2.1 percent growth in 2019, well below the White House estimate, and just 1.9 percent growth in 2020.
In the Bloomberg Television interview, Moore said he was "not sure" about whether the Fed should cut rates and also said he needed to "reserve judgement" about the size of the Fed's bond holdings "because I don't have the full knowledge that I need".
French President Macron Urges EU to ‘Confront US, China’
The Trump administration is engaged in ongoing trade talks with both the European Union and China as part of the Republican president's "America First" agenda.
Also under consideration for the Fed board is Herman Cain, who ran for the 2012 Republican presidential nomination, the Bloomberg reported Thursday, citing anonymous sources.
At the end of a two-day policy meeting, the Federal Open markets Committee (FOMC) said the move was meant to meet market expectations and reflected the central bank's patient approach regarding monetary policy changes.
" Janet Yellen couldn't have been any worse than the guy he's got in there now", Moore said of Powell and his predecessor. Moore proposed that the Fed set short-term rates with an eye toward stabilizing commodity prices, rather than exclusively on overall inflation.
The choice of Moore drew broad criticism, as economists across the spectrum noted that Moore's writings and comments seemed to confuse basic concepts, and had been wildly inconsistent over time.
The nomination, which is subject to Senate approval, would elevate someone to the Fed who has, like Trump himself, been a big critic of the central bank. "The law is clear that I have a four-year term, and I fully intend to serve it", he said.
He co-wrote a book with Trump's name in the title: 'Trumponomics: Inside the America First Plan to Revive our Economy'.
But federal debt has jumped since Trump's overhaul to the tax code, surging almost 77 per cent through the first four months of fiscal 2019 compared with the previous year.