Several months ago, when it was still conventional wisdom that Trump wanted to replace Janet Yellen - at least until Trump's famous WSJ interview in which he flipped on this and various other issues - with a hawk once her tenure runs out in 2018, the financial punditry was busy coming up with potential replacement names, a practice which gradually faded away once it emerged that Trump may well keep Yellen.

That changed today when in a note by Beacon Policy Advisors, a new name emerged which according to CNBC has set Wall Street abuzz. That name is that of former Goldman COO and current Trump National Economic Council advisor Gary Cohn.

"The buzz among those who claim Cohn confides in them is that he would like to eventually replace" Yellen, assuming Trump decides to move in a different direction when the chair's term ends in early February, Beacon Policy Advisors said in its daily report for clients Tuesday, cited by CNBC's Jeff Cox.

"On paper, Cohn likely meets Trump's expected top two requirements for a Fed chair candidate," the Beacon analysis said, specifically citing Cohn's advocacy for deregulation and his likelihood to keep interest rates low as Trump seeks to implement his pro-growth economic policies.

As Cox notes, while during his presidential campaign Trump openly criticized Yellen, accusing her of keeping interest rates low and using monetary stimulus to prop up the economy under Obama, "he's been relatively mum about Yellen since taking office in January. He also has emphasized the need for a cheap dollar and low interest rates as the economy seeks escape velocity from an extended period of low growth."

"If Trump wants rates to be as low as possible, (Yellen's) still the best choice," said Greg Valliere, chief global strategist at Horizon Investments and a widely followed expert on the Wall Street-Washington connection. "In my career, I've never seen a president who favored higher interest rates. That's pretty unusual."

To be sure, who better to do that than the former Goldman Sachs #2. In many ways it would be a logical progression: with Goldman alumni already in charge of many central banks, either directly or indirectly - former Goldman MD Bill Dudley runs the New York Fed, while former Goldmanites run the BOE and ECB - it would be perfectly fitting that Trump would complete his metamorphosis to an establishment politician by appointing a Goldman banker to run the Fed directly.

According to sources cited by CNBC Cohn is among the top contenders, along with former Fed Governor Kevin Warsh and FDIC Vice Chair Thomas Hoenig, to replace Yellen.

"He's the leading contender," said Christopher Whalen, an insider in the banking world and currently head of Whalen Global Advisors. "Every Fed chairman in recent memory going back even to (Paul) Volcker went through the White House in one way or the other. ... It would certainly make sense." Whalen said he personally favors Warsh for the position but believes Cohn "wouldn't be a bad choice." Whalen thinks Cohn would "have no choice" but to advocate for keeping rates low during what Whalen believes will be an economic slowdown ahead.

A White House spokeswoman said the chatter was "entirely speculation" and called the Beacon report and any others "inaccurate."

Cox notes that there are several negative considerations to picking Cohn.

Most notably, the president is relying on Cohn to usher his economic agenda through Congress and help with the implementation, particularly regarding tax reform. If Trump can't get a tax plan passed by next February, that would make it tougher to let go of Cohn. Moreover, CNBC recently reported that Cohn actually may have pushed Trump to keep Yellen on board. However, it's not clear whether Yellen, 70, even would want to be given another them.

Should Yellen would want to leave, however, Cohn, along with Hoenig, Warsh and John Taylor, "would certainly be on the short list," Valliere said. "Cohn would be an interesting pick, though there would be some concern that he was politicized and the markets could view him with some suspicion that he is too close a political ally with Trump."

Then there's the obvious Goldman connection. While Cox correctly notes that Critics "have ripped into Trump for perpetuating the "Government Sachs" culture in Washington where so many of the firm's principals have found their way into high levels of government" that does not appear to be bothering Trump much in recent weeks.

Beacon concluded that "it remains unclear though, especially this many months in advance of Yellen's term ending, as to whether there will be sufficient support for Cohn for this role within the West Wing at that time and whether he could even get confirmed given his lack of conservative credentials and academic background, not to mention his prominent ties to Goldman Sachs."

However, the fact that this particular trial balloon is being floated so early to set the stage, likely implies that the probability of a former Goldman president becoming Fed chair is far higher than most would suspect.