Mr. Quarles is regarded as significantly more sympathetic than Mr. Tarullo to the industry’s concerns that regulation is overly restrictive, limiting economic growth.

In a 2015 interview with Bloomberg Television, he said some postcrisis changes in regulation “aren’t well designed and were included for political rather than financial-regulatory reasons.” In a 2016 opinion piece in The Wall Street Journal, Mr. Quarles argued that it was misguided to focus on the size of the largest banks.

One of Mr. Quarles’s major tasks at the Fed would be overseeing the annual “stress test" of large banks, intended to make sure that they can weather a crisis.

But his influence would be constrained, at least in the short term, because Ms. Yellen played a key role in developing those regulations. Ms. Yellen’s term ends in February 2018, creating the next Fed personnel decision confronting Mr. Trump.

Mr. Goodfriend, 66, is a leading figure among conservative economists who study monetary policy. He worked for more than 20 years as an economist at the Federal Reserve Bank of Richmond; for more than half of that time, he was the chief monetary policy adviser to the bank’s president, a member of the Fed’s policy committee.

He left the bank in 2005 to join the faculty at Carnegie Mellon University.

Mr. Quarles and Mr. Goodfriend have expressed support for the idea that the Federal Reserve should adopt a more formulaic approach to policy-making. House Republicans have proposed legislation that would require the Fed to articulate a policy rule — a mathematical approach to determining the level of interest rates — that would limit the role of human judgment in monetary policy.

“If you’re going to be transparent in an activity like the Fed, you have to be much more rule-based in what you’re doing,” Mr. Quarles told Bloomberg Television in 2015. He described the Fed’s current approach as “a crazy way to run a railroad.”