Warsh had strong words about his commitment to fighting inflation.
Oil prices have surged in recent weeks, threatening wider inflation.
A federal judge blocked subpoenas issued by the Justice Department against Fed Chair Jerome Powell after determining the government "produced essentially zero evidence."
Trump said his pick to replace current Chairman Jerome Powell is an "outstanding person and a person that won't be too surprising to people."
The Federal Reserve held interest rates steady on Wednesday, as the central bank grapples with a combination of elevated inflation and sluggish hiring.
The Supreme Court seemed inclined to keep Federal Reserve governor Lisa Cook in her job, casting doubt on President Trump's bid to wrest control of the nation's central bank.