President Donald Trump appears ready to remake the Federal Reserve in an image that will be considerably different than what investors have known for many years.

The president is prepared to nominate Randal Quarles and Marvin Goodfriend to two of three vacancies at the central bank, according to multiple press accounts that have not been disputed by the administration. Quarles likely would assume the role vacated by Daniel Tarullo to oversee the nation's banking system. White House officials did not respond to a CNBC request for comment.

Should Trump nominate the two men and they receive confirmation, it will represent the first steps in a possible substantial remaking of a Fed that has practiced ultra-loose monetary policy for the past decade but has been tight on banking regulations.

Trump will have the opportunity to name one more person now, then can fill two even more critical vacancies in 2018 — that of Chair Janet Yellen and Vice Chair Stanley Fischer.

If the Quarles and Goodfriend moves are indicators of what's to come, things could start getting less comfortable for Yellen. Both are considered solidly conservative, in line with the Republican president and Congress but perhaps not with Yellen.

"Clearly, these appointees are a significant departure from the crowd that we've had on the board," said Christopher Whalen, head of Whalen Global Advisors and a former investment banker and long-time financial analyst. "Yellen is probably the most left-wing Fed chair we've ever had. I also think both Quarles and Goodfriend have much better grounding in the financial markets. That would be refreshing."

Yellen, however, may not think so, particularly if the coalition she has carefully crafted since taking the chair's seat in 2014 starts to unravel.

"I welcome these additions," Whalen said. "Hopefully they put a banker in the third slot. Then eventually Yellen's going to leave because she's going to start losing votes."