In August, 15 progressive groups wrote Clinton a letter urging her to steer clear of Wall Street when making appointments to the administration. Bloomberg first reported on the letter.
"Historically, too many Wall Street executives and corporate insiders have traveled through the revolving door between private industry and government," the groups wrote. "Only months removed from lucrative past or future positions, they have been granted influential positions in the upper echelons of presidential administrations. They are often offered, and receive, massive golden parachute bonuses from their past employers for taking these government positions. The result of this practice is that the interests of elites are over-represented in Washington."
"I think it's highly, highly unlikely that she'd appoint a Treasury [Secretary] with a Wall Street background, with the exception of someone like Gary Gensler who not only has a solid record of prosecuting financial market excesses, but is already close to the candidate," said Jared Bernstein, a senior fellow at the Center on Budget and Policy Priorities and outside economic advisor to Hillary Clinton.
Gensler, a former Goldman Sachs executive, gained a reputation as a hard-charging regulator while chairing the Commodity Futures Trading Commission (CFTC).
Another top prospect for the job if Clinton is elected is Federal Reserve Board Governor Lael Brainard, who was previously under-secretary of the Treasury for international affairs. Brainard doesn't have vast Wall Street experience, but some Democratic progressives worry that her nomination could signal bad news for the middle class given her past support of free trade deals.
Some economists aligned with the Clinton campaign disagree.
"For progressives to exclude Lael Brainard — someone who has the broad knowledge and experience to lead the Treasury successfully is foolish" said Betsey Stevenson, a professor at the University of Michigan's Gerald R. Ford School of Public Policy and who sometimes advises the Clinton campaign on such matters.
"It's important for progressives to realize that another severe recession would do a lot to hurt progressive causes and an experienced steady hand is crucial when it comes to weathering storms," said Stevenson, a former member of President Obama's Council of Economic Advisers.
Other advisers to the Clinton campaign argue that picking someone with vast policy experience like Brainard may be the wisest route, as such an individual will be highly valuable in case there's another global economic crisis.
From Sylla's perspective, the next Treasury secretary has a huge job ahead of him or her, one that includes includes keeping national debt levels low and monitoring the strength of the U.S. dollar.
"Any good candidate or nominee for the position, regardless of background, should have a really good understanding of these important functions and the self-confidence not to be bullied or pushed around by others with particular political agendas," Sylla says.
Steve Moore, a distinguished visiting fellow at the Heritage Foundation, told NBC News that ruling out business and finance mavens for Treasury secretary would be a huge mistake.