President Trump is reportedly planning to nominate a Carnegie Mellon professor and proponent of monetary reforms favored by conservatives to an open spot on the Federal Reserve's Board of Governors, which is currently understaffed by three.

Trump aims to nominate Marvin Goodfriend, a former economist at the Federal Reserve Bank of Richmond, to one of the three open governor positions, The New York Times reported Friday.

Along with Goodfriend, Trump favors former George W. Bush Treasury official Randal Quarles for another of the governor positions and to serve as vice chairman for supervision, an important role in shaping regulation of the financial system. The administration's plans to nominate Quarles had previously been reported by other publications.

Quarles would effectively replace Daniel Tarullo as the Fed's point man on financial regulation. Tarullo, who stepped down in April after serving since 2009, played a lead role in implementing post-crisis regulations and pushing for more restrictive rules than required by law or mandated in international agreements. Tarullo, though, was never nominated as vice chair for supervision. In fact, that post has not been filled since it was created in 2010.

As members of the Board of Governors, Goodfriend and Quarles would both vote on both monetary policy decisions in addition to carrying out the Fed's regulation and supervision of banks.

Goodfriend has expressed support for the idea of the Fed spelling out a rule tying its monetary policy decisions to incoming economic data. That idea, popular among House Republicans, would not necessarily require the Fed to take a specific course of action, but rather would mandate that it compare its monetary policy conduct to a predictable rule.

Republicans have said that such a reference rule would bring clarity and predictability to the Fed's interest rate decisions. Current Fed members, however, including Chairwoman Janet Yellen, have criticized the idea as introducing too much political influence to monetary policy decision-making.

Any appointments of Trump's would serve under Yellen, which would limit their ability to shape policy. Yellen's term as chairwoman runs through February. Although a nomination would be expected this summer if the administration planned to replace her with an appointment of its choosing, the White House has not indicated whether it aims to do so. Asked Friday in an interview with Bloomberg TV if Trump plans to appoint someone else, National Economic Council Director Gary Cohn declined to comment.