The expected nominees include Randal K. Quarles, a Treasury Department official in the George W. Bush administration, and Marvin Goodfriend, a former Fed official who is now a professor of economics at Carnegie Mellon University. The name of the third nominee could not be confirmed.
In picking Mr. Quarles and Mr. Goodfriend, President Trump is seeking to install conservative counterweights to the Fed's chairwoman, Janet L. Yellen. Both men have expressed reservations about the Fed's aggressive efforts to revive economic growth since the 2008 crisis.
Mr. Quarles would also become a leading figure in the administration's efforts to roll back financial regulation. He would be nominated to serve as the Fed's vice chairman for supervision, with responsibility for overseeing the Fed's regulatory responsibilities.
It is not clear when the administration intends to announce the nominations, according to the people, who requested anonymity to discuss confidential conversations. Until that happens, it remains possible that Mr. Trump could decide to reopen the search process.
Mr. Quarles and Mr. Goodfriend did not return calls requesting comment. "We have no announcement at this time," said Lindsay Walters, a White House spokeswoman.
Mr. Quarles, 59, is a managing director at the Cynosure Group, a private equity firm based in Salt Lake City. His wife's great-uncle is Marriner Eccles, the Fed's chairman from 1934 to 1948 and the namesake of the Fed's marble headquarters on the National Mall in Washington, where Mr. Quarles would have an office.
Mr. Quarles was a lawyer for the financial industry before joining the Bush administration in 2002, first as assistant secretary for international affairs and then as under secretary for domestic finance. After leaving the administration in 2006, he became a partner at the Carlyle Group before helping to found Cynosure in 2014.