The Fed chairman also plays a leading role in financial regulation and will have to navigate calls by Republican leaders, including Mr. Trump, to roll back some of the rules put in place after the 2008 financial crisis. Ms. Yellen was a principal architect of those more stringent regulations and has said the financial system is much stronger as a result. Mr. Trump has criticized many of the banking rules, saying they are excessive and impeding economic growth. The candidates to replace Ms. Yellen all share those concerns to varying degrees.
Given the high stakes, Mr. Trump’s decision has become a source of intrigue in political and economic circles this year. There is also a growing sense of urgency: Both Ms. Yellen and her predecessor, Ben S. Bernanke, were nominated in October, leaving ample time for the Senate to hold confirmation hearings. Mr. Trump has said he does not plan to make a decision until later in the year, leaving little time for the Senate to act given the tight calendar. Aides say he is not yet focused on the search. Additional candidates could ultimately be considered.
The administration officials and the other person with knowledge of the search requested anonymity because of the sensitive nature of the job in question. A White House spokeswoman had no immediate comment, and Mr. Cohn, Mr. Taylor and Mr. Warsh did not respond to requests for comment. A Fed spokeswoman said Ms. Yellen and Mr. Powell declined to comment.
The next Fed chairman is likely to begin the four-year term in an atmosphere of relative tranquillity during one of the longest economic expansions in American history. But the Fed is confronting a number of difficult issues. One question is whether it can do more to increase economic growth. Another is whether the Fed will be ready for the next economic downturn.
In addition to a Fed chairman, Mr. Trump also must fill four open seats on the seven-member board. That means he can immediately appoint a majority of Fed governors, putting his stamp on the institution. He has made just one choice so far, nominating Randal K. Quarles to be the Fed’s vice chairman for supervision. That nomination is pending, though Mr. Quarles is expected to be confirmed.
Mr. Trump has deputized four officials to lead the selection process for the Fed’s next chairman, said one person familiar with the search: Treasury Secretary Steven Mnuchin; two of Mr. Cohn’s aides on the National Economic Council, Jeremy Katz and Andrew Olmem; and John DeStefano, the White House personnel director.
Mr. Cohn, who initially participated in conversations about the potential nominees for Fed governor seats, has removed himself from the discussions about the central bank’s next chairman, given that he is a potential candidate for the job, said several people with knowledge of his involvement.
Mr. Cohn left the No. 2 position at Goldman Sachs to join Mr. Trump’s administration as head of the National Economic Council. He quickly developed an easy rapport with the president, who is said to value Mr. Cohn’s knowledge of markets and finance. Mr. Cohn has played a major role in the administration’s push for a tax-cut bill; he also has been a moderating voice in internal debates on issues like restricting free trade.
In a July interview with The Wall Street Journal, Mr. Trump described Mr. Cohn and Ms. Yellen as candidates for the Fed job. The next month, Mr. Cohn publicly criticized the president’s response to a white nationalist rally in Charlottesville, creating tension. But the two men have reestablished a comfort level, and Mr. Cohn remains a candidate.
Mr. Cohn is a strong advocate for easing financial regulation, which he argues is unnecessarily impeding economic activity. But he has rarely spoken publicly about monetary policy; the other four candidates whose names are known all have significant experience with monetary policy.
Mr. Warsh, who served on the Fed’s board between 2006 and 2011, was a member of Mr. Trump’s business advisory council and has informally advised him on a range of economic issues. That may be a significant advantage, given the president’s demonstrated preference for people he knows and trusts. Mr. Warsh is married to Jane Lauder, the daughter of Ronald Lauder, a friend and occasional adviser to the president.
Mr. Warsh is a lawyer by training and a banker by trade before entering public service in 2002 as a member of President George W. Bush’s National Economic Council. After leaving the Fed, he joined the Hoover Institution, a public-policy think tank run by Stanford, as a visiting fellow. He has been a vocal critic of the Fed’s economic stimulus campaign under both Mr. Bernanke and Ms. Yellen, arguing it has been ineffective and may have dangerous side effects.
At a Hoover conference in May, he said the Fed needs to be “aggressive and powerful” in responding to financial crises, but remain “more traditional” when the market is not in crisis.
Mr. Taylor, a colleague of Mr. Warsh’s at Hoover, has offered a similar critique of Fed policy. Mr. Taylor served in the Treasury Department during the Bush administration but he is best known as an academic economist. He wrote a formulaic approach to monetary policy, known as the “Taylor Rule,” which suggests that the Fed should be raising rates more quickly. He also has closely advised House Republicans on legislation that would require the Fed to adopt such a policy rule.
Mr. Powell, the only Republican on the Fed’s board, is regarded as a centrist voice on both monetary policy and regulatory issues. In internal discussions and public remarks, he has sometimes pushed back against the most ardent supporters of the Fed’s postcrisis stimulus campaign. Similarly, he has sometimes raised questions about changes in financial regulation. But on both fronts he has consistently voted with the majority.
A Treasury Department official under President George H.W. Bush, Mr. Powell then built a fortune as a partner at the Carlyle Group, a private equity firm, before he was nominated to the Fed by President Obama in 2012. His experience at the Fed, and his connections both in the financial world and in the Republican Party, could make him an attractive candidate. But his track record suggests he may be less likely than some of the other candidates to press for dramatic changes in monetary and regulatory policies.