There are currently three open Federal Reserve Board of Governors positions and the New York Times reports that Trump is ready to nominate the following two:
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.
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.
Importantly for the discretionary vs. rule-based policy debate, it seems that Trump and those advising him are specifically picking two people who have been outspoken in defense of rule-based (such as the famed Taylor Rule) decision making. This is in contrast to Stanley Fischer and others at the current the Fed who have been firm in defense of discretionary policies.
We still await a formal announcement from Trump.