Williams' appointment has not been confirmed officially — "Nothing is final," a New York Fed spokesman said.

Some worry, for instance, that the move could be another blow against efforts to get a more diverse look among the policymakers who run the Fed, while others see his resume darkened by banking controversies that happened under the nose of the San Francisco Fed, where Williams has worked since 2002. He became president there in 2011, succeeding Janet Yellen, who a few years later went on to become Fed chair.

While Williams carries a wealth of experience from a Fed career that began in 1994, his appointment could stir controversy from a number of angles. Williams would replace William Dudley, who announced his retirement effective around midyear.

A committee that has been looking to replace William Dudley at the central bank's critical New York branch apparently has centered in on Williams as a successor, sources have told CNBC .

John Williams' cross-country path from the San Francisco to the New York Fed could be a bumpy one.

Sen. Elizabeth Warren, a Massachusetts Democrat who has been a staunch banking critic, particularly on issues relating to the Wells Fargo fake account scandal, said she wants a chance to grill Williams before he is appointed.

"Mr. Williams' track record raises several questions, including about his fitness to supervise Wall Street banks given the San Francisco Fed's inadequate supervision of Wells Fargo during its many consumer scandals," Warren said in a statement.

"If Mr. Williams is selected, the Fed's Board of Governors should not approve his selection until Mr. Williams and the co-chairs of the New York Fed's search committee testify before the Senate Banking Committee about his qualifications and the process that led to his selection."

The San Francisco Fed has been tarred with the fallout from the Wells Fargo problems. Also, Washington Mutual, which was in the San Francisco jurisdiction, was one of the highest-profile bank collapses during the financial crisis, and much of the savings and loan crisis of the late 1980s revolved around the region.

While it would be hard to place the blame for any of those failures directly at Williams' feet, his appointment still brings up reminders of a darker place in American banking history.

Wells Fargo employees, pressured by aggressive sales quotas that have since been abandoned, created some 3.5 million accounts without customer knowledge. Several high-ranking bank officials were pushed out, as were multiple board members.

"I do know the San Francisco Fed, which gave us Janet Yellen as well, has perhaps overly focused on the monetary and economic functions of the Fed and completely ignored or failed to understand the regulatory functions," said Dick Bove, analyst at the Vertical Group. "So they have given the United States some of the worst financial disasters in history."

A number of Warren's Senate colleagues have bemoaned the lack of diversity among top officials that they say has led to discriminatory lending and housing policies.

The New York Fed plays a key role on a number of fronts. Its bond trading desk helps maintain the level for the Fed's target funds level, its benchmark rate connected to most consumer debt, and it also plays a key role in policy.

An official at the San Francisco declined comment. The New York Fed did not respond to a request.

Correction: Wells Fargo employees created some 3.5 million accounts without customer knowledge. An earlier version misstated the figure.