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That mix of qualities is not easy to find.

“I think Trump has a problem in that he wants two different things,” said Lawrence H. Summers, who served as Treasury secretary in the Clinton administration. “He wants somebody who will be deeply loyal, and he wants someone who will be deeply reassuring to markets. Since markets are fearful of the tariff agenda, it’s hard to square both things.”

In recent days, Mr. Trump has been considering several candidates for the job, and their prospects have been rising and falling by the hour, according to people familiar with the deliberations.

The current front-runners are Scott Bessent, the billionaire hedge fund manager, and Kevin Warsh, a former Federal Reserve governor. Marc Rowan, the chief executive of Apollo Global Management, is also in the running, while Howard Lutnick, Mr. Trump’s transition co-chairman and the chief executive of Cantor Fitzgerald, appeared to fall out of favor for that post and was tapped on Tuesday to serve as commerce secretary instead.

Mr. Trump has made unorthodox choices for some cabinet posts. But a Treasury secretary pick who is seen as unserious could rattle markets and impede his ability to deliver on his economic promises. For that reason, Mr. Trump needs a secretary who is respected in corporate America and can strike a balance between supporting tariffs while not seeming eager to start a trade war that could tank the global economy.

“Investors are on edge regarding the Trump Treasury secretary pick and what it might signal about the balance of power within the administration on economic policy, the mix of market-friendly versus -unfriendly policies, and how less market-friendly trade and immigration policies plus deficits will be calibrated to mitigate adverse impacts,” analysts at Evercore ISI wrote in a note to clients this week.

Analysts at the research group Beacon Policy Advisors theorized on Tuesday that Mr. Trump had the stock market in mind as he considered his decision. They noted that one reason Mr. Trump had not selected Robert Lighthizer, his trusted former trade representative and the architect of the tariffs in his first term, was that the president-elect was mindful of the effect that the choice would have on markets.

“Ultimately, Trump will likely select a nominee who can sell his tariffs to the markets rather than mitigate them,” they wrote in a report analyzing the stakes of the decision. “When it comes to Trump, tariffs can be seen as an end goal in themselves.”

Although the Treasury secretary does not direct trade policy or enact tariffs, the person in the role is generally the economic face of an administration whose goal is to instill confidence in the U.S. economy. The Treasury secretary is expected to explain America’s economic policies to companies and investors around the world, helping to ensure that investment flows into the United States and investors continue to see its debt as a solid investment.

The Treasury Department is at the core of the federal government and issues debt to fund the nation’s operations and pay its bills, including paying Social Security and veterans’ benefits. Although the American economy is the strongest in the world, the national debt is approaching $36 trillion, and prices remain high after two years with record levels of inflation.

“Whoever becomes Treasury secretary will face a full plate and daunting challenges, including making the case for large tax cuts, which will cause a huge explosion in debt and deficits, dealing with the Fed — and perhaps combatively so — on behalf of the president,” said Mark Sobel, a longtime former Treasury official.

He added that Mr. Trump’s Treasury secretary will also have to deal with “jousting over the dollar and exchange rate policy with noisy White House and trade teams calling for devaluation.”

Mr. Trump has often said that, for the sake of U.S. exports, he would prefer to see the dollar weaken because that would make American goods cheaper to buy overseas. But most economists expect his plans to impose tariffs on imports and cut taxes, among other actions, to have the opposite effect.

The day after the election, the dollar rose the most it had in years against a basket of other major currencies. And it has continued to rise, hitting a fresh high for the year last week.

Mr. Trump’s victory also has led to unease among bond investors, who worry about government largess and the resurgence of inflation under the president-elect. That has led to a rise in bond yields, which means investors expect to be paid more in interest in exchange for lending to the government.

A booming stock market is another priority for Mr. Trump, who sees stock prices as a critical indicator for the health of the economy. However, during Mr. Trump’s first term, each new round of tariffs that he imposed on Chinese imports sent stocks falling.

That dynamic is likely to play out again, as Mr. Trump has called for blanket tariffs as high as 50 percent on imports and even higher tariffs on goods from certain countries.

“Tariffs are going to increase costs on a lot of U.S. multinationals” said Brad Setser, a senior fellow at the Council on Foreign Relations. “The conventional wisdom is that would make many in the market nervous.”

Mr. Setser, who served as the deputy assistant secretary for international economic analysis at the Treasury Department from 2011 to 2015, said that the desire for a rising stock market and higher tariffs were “somewhat in tension” and that Mr. Trump’s Treasury secretary will have to grapple with those crosscurrents.

As Mr. Trump and his advisers have been considering that pick, a belief in the merits of tariffs has been a priority. Mr. Trump’s first Treasury secretary, Steven T. Mnuchin, often argued against increasing tariffs on China and warned about the potential market implications.

That has put the views of the current group of front-runners in focus.

Mr. Warsh argued in a 2011 Wall Street Journal essay written with Jeb Bush, the former Florida governor who ran against Mr. Trump in 2016, that “we must find our voice to resist the rising tide of economic protectionism.”

Mr. Bessent has suggested recently that Mr. Trump’s tariff threats are a “maximalist” negotiating strategy to secure better free trade deals, and he has expressed concern about flouting World Trade Organization rules. Those comments led some of Mr. Bessent’s detractors to argue that he is not a true believer in tariffs or, as the increasingly influential billionaire Elon Musk recently said, is “a business-as-usual choice.”

“Business-as-usual is driving America bankrupt, so we need change one way or another,” Mr. Musk, who expressed support for Mr. Lutnick to get the job, wrote on social media on Saturday.

For Mr. Trump, the decision could come down to whom he most trusts to be loyal.

Stephen Moore, a Heritage Foundation economist who advised Mr. Trump’s first campaign, said that Mr. Trump benefits from aides who will try to steer him away from making mistakes but that he has learned to prioritize hiring people who believe in his policies. That is especially true, he said, when it comes to tariffs.

“If you’re going to go in and work for Trump, you’ve got to be on board with the agenda,” Mr. Moore said.