President-elect Donald J. Trump is now exploring additional options for the role of Treasury Secretary, as internal discussions continue to shape his decision. Among the new contenders is Kevin Warsh, a former Federal Reserve governor.

Also under consideration is Marc Rowan, a billionaire from Wall Street.

Previously, Mr. Trump was expected to choose between Howard Lutnick, the CEO of Cantor Fitzgerald, and Scott Bessent, founder of Key Square Capital Management and a former money manager for George Soros. Speculation suggested a decision might have been made late last week.

However, Mr. Trump appears to have reconsidered these top candidates, causing a delay in the selection process. He plans to interview the finalists, including potential new names, this week at his Mar-a-Lago estate.

Tensions have arisen around Mr. Lutnick, who is leading Mr. Trump’s transition team. Reportedly, Mr. Trump has grown frustrated with Mr. Lutnick’s frequent presence and perceived attempts to manipulate the process for personal gain. An anonymous source described the competition between Mr. Lutnick and Mr. Bessent as highly contentious, with Mr. Lutnick being particularly aggressive.

Mr. Bessent remains in the running and has also been floated as a potential head of the National Economic Council. On Sunday, Elon Musk, a close adviser to Mr. Trump, referred to Mr. Bessent as a “business-as-usual” choice for Treasury Secretary on X, his social media platform, while endorsing Mr. Lutnick.

Mr. Trump met with Mr. Lutnick on Sunday, though the outcome of their discussion remains unclear, according to sources familiar with the matter. Mr. Bessent has also met with the president-elect, and additional candidates, including Mr. Warsh and Mr. Rowan, are expected to have discussions with Mr. Trump this week.

Karoline Leavitt, the incoming White House press secretary, declined to elaborate, stating only, “President-elect Trump is making decisions on appointments for his second administration, and announcements will be made as they are finalized.”

Mr. Trump has indicated he wants a high-profile individual for the Treasury role, placing a premium on wealth and status within Wall Street circles. He has expressed particular admiration for Mr. Rowan, CEO and co-founder of Apollo Global Management. At the same time, Mr. Trump has praised Mr. Warsh for his intelligence and appearance.

Mr. Warsh has been frequently mentioned as a potential Federal Reserve chairman. Although Jerome H. Powell currently holds that position, his term expires in 2026. Mr. Trump had previously considered Mr. Warsh for the role in 2017 but ultimately chose Mr. Powell, a decision he later regretted due to policy disagreements.

“I could have used you a little bit here,” Mr. Trump told Mr. Warsh during a 2020 press conference, adding, “I would have been very happy with you.”

The deliberate pace of this Treasury Secretary decision contrasts sharply with Mr. Trump’s swift action on other major cabinet appointments. His concern over the impact of this choice on the stock market has contributed to the delay, as he seeks to maintain market momentum following his election victory.

This caution has ruled out Robert Lighthizer, a former trade adviser whose tariff policies might unsettle the markets. Nonetheless, Mr. Lighthizer could still be considered for another economic or trade-related role.

At the same time, Mr. Trump aims to avoid appointing someone who might resist his populist economic agenda, as Steven Mnuchin, his first-term Treasury Secretary, sometimes did. Among the current candidates, Mr. Lutnick has been particularly outspoken in favor of tariffs.

Given Mr. Trump’s indecision, those close to him acknowledge that another contender could still emerge.

Representatives for Apollo, Mr. Warsh, Mr. Bessent, and Mr. Lutnick either declined to comment or did not respond to inquiries.