John Allison, the man who could be Donald Trump's bank chief

American banks likely will have a new chief regulator soon, with one of the most likely candidates a welcome name to Wall Street.

John Allison is a name frequently mentioned when it comes to potential candidates President-elect Donald Trump is considering to run the nation's financial system, though a handful of other names also have been bandied around.

If the chatter about him is true, Allison would be named for a Federal Reserve Board of Governors vacancy that would make him vice chairman and head of banking regulation, a position left technically unfilled since it was mandated by the Dodd-Frank banking reforms.

The Trump camp did not respond to CNBC requests for comment.

The Street knows Allison well: He was CEO of BB&T from 1989 to 2008 and developed a reputation as a strong hand who guided the bank through years of prosperity and kept the institution off the rocks when the financial crisis hit in 2008. During his tenure, BB&T's assets swelled from $4.5 billion to $152 billion. The bank now has more than $217 billion in assets and is the 11th-largest U.S. institution.

In addition, he followed up his time there at the libertarian Cato Institute think tank, where he currently serves on the board after being president and CEO from October 2012 to April 2015.

Appointing Allison as a Fed governor would carry some irony: A few months ago he told CNBC he would, at least theoretically, like to disband the U.S. central bank, though he knows it's not "doable in practice."

"What I really want to do with the Federal Reserve is control it," he said in late November. "You really have an incredibly powerful organization that there's no self-discipline for, and it's had a big impact, I believe, on our economic volatility over the years."

Allison was unavailable Tuesday for further comment.

He may well get the opportunity to help reshape the Fed, though he also had been in the running for Treasury secretary at one point. The other most serious contenders appear to be Thomas Hoenig, himself a former Fed official and currently vice chair of the FDIC, and John Taylor, the Stanford economist and developer of the oft-cited Taylor rule for where interest rates should be based on economic indicators.

If Trump does tap Allison, they would share neatly matching visions of what the Fed's role should be. Like Trump, Allison opposes the Dodd-Frank banking reforms. But also like the president-elect, Allison believes in a no-nonsense approach to banks that become systemically dangerous.

"We need to stop putting economists on the board. The reason we have too-big-to-fail is because the economists are afraid to close down bad banks," said Christopher Whalen, senior managing director and head of research at Kroll Bond Rating Agency and once a rumored candidate himself for the position. "Having Allison in there, who's unafraid and unapologetic when it comes to his views on this, would be outstanding."

Industry groups likely would welcome Allison.

"It's good that there's more recognition that the Fed needs to have people on the board with banking experience," said one trade group official who spoke on condition of anonymity because the organization does not publicly comment on potential nominees.

The assumption with the appointment of the new Fed bank regulator is that the current unofficial holder of the position, Daniel Tarullo, would resign. Fed officials speaking on Tarullo's behalf Tuesday declined comment.

Wall Street executives and analysts have long complained that the current climate at the Fed and in Washington generally has been one of overarching restrictions on risk since the financial crisis, which was precipitated in large part by reckless lending practices.

Since then, banks have rebuilt their capital base and have $1.86 trillion in excess reserves stored at the Fed. A new regulator who seeks to reopen the financial spigots in the banking system would be welcome.

"Mr. Trump wants to focus on rebuilding America's manufacturing capabilities," Dick Bove, vice president of equity research at Rafferty Capital Markets, said in a note. "This is Mr. Allison's greatest strength. He has already done this. He made over 100 acquisitions. He created tens of thousands of jobs at BB&T and he loaned out tens of billions of dollars."

In addition to promoting a more robust banking climate, a Fed governor the likes of Allison also would give Trump the opportunity to influence the Fed's overall direction. Trump was critical of current Fed Chair Janet Yellen during the presidential campaign, though he's been mostly mum on the topic since the election.

"Trump is inclined to appoint critics of Janet Yellen, and I would view this as part of his long-range plan to get rid of her," said Greg Valliere, noted political observer and chief global strategist at Horizon Investment. "The signals he'll send is he wants to totally reshape the Fed, and she will not play a part in that exercise."