Moore, who formerly served as chief economist for the conservative Heritage Foundation, has also been critical of policy moves made by Chairman Jerome Powell, who was hand-picked by Mr. Trump to be Fed chairman.
The group often reach policy decisions by consensus after debating the issues.
"Steve is a perfectly amiable guy, but he simply does not have the intellectual gravitas for this important job", said Harvard economist Gregory Mankiw, who chaired the Council of Economic Advisers under President George W. Bush.
The Fed's key benchmark rate is now 2.25 to 2.5 percent.
Moore, 59, previously served as a Trump 2016 campaign adviser and is now a visiting fellow at the Heritage Foundation. Trump wrote on Twitter on Friday.
"I am open to all possibilities as we aim to support sustained economic expansion, strong labor market conditions, and inflation near the Committee's symmetric 2 percent objective", Bostic said, referring to the policy-setting Federal Open Market Committee. "I have no doubt that Stephen Moore would make an excellent member of the Federal Reserve Board".
Moore founded the Club For Growth, a conservative group that funded an ad blitz in 2016 meant to stop Trump from winning the Republican presidential nomination. He did not say how many rate hikes he now thinks are appropriate.
Given his sharply partisan reputation, Moore could spark opposition among Democrats in the Senate.
Under fire from Trump, Powell has tried to communicate directly to a broader audience of Americans, appearing on the CBS News programme 60 Minutes and doing town-hall discussions in an effort to demystify what his institution does. None of the other members of the committee commented when contacted by Reuters about Moore's nomination. But we would have been over four (per cent growth) if they didn't do all of the interest rate hikes.
When the dot plot shifts, it can send a powerful message to investors on whether the US central bank expects to speed up or slow down its planned tightening of monetary policy.
But he added, "over time obviously we want to reduce that balance sheet and not have these massive amounts of debt".
The Fed on Wednesday said it would stop scaling back the vast portfolio of bonds they built up to spur an economic recovery from the 2007-2009 financial crisis and recession.
Although Trump picked Powell to lead the Fed, starting in February 2018, it didnt take long for him to regret his decision.
Moore joined CNN as a contributor in early 2017. In the article Moore argued that the Fed's rate hikes promoted deflation and described the central bank as the "last major obstacle" to the United States staying on a good path.
Trump in his first two years in office has been able to reshape the central bank. And he contended that the approach, if adopted, would help accelerate economic growth above 3 percent, compared with the longer-run average of 1.9 percent that Fed officials have forecast.
The spread between yields on three-month Treasury bills and 10-year notes fell below zero for the first time since 2007 after USA manufacturing data fell short of estimates.
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