Members of President Biden’s economic team generally support nominating Federal Reserve Chairman Jerome Powell to a second term, but growing resistance from prominent Democrats including Sen. Elizabeth Warren (D., Mass.) could lead to his replacement, according to people familiar with the matter.

Mr. Powell, who was appointed to his first term by former Republican President Donald Trump, has received high marks from some Democrats for steering the central bank toward a paradigm shift that has placed greater attention on reducing unemployment. That coincided last year with a forceful response to the coronavirus pandemic.

But some progressives are unhappy with his bent toward easing financial regulations that were put in place after the 2008 crisis and think the central bank should have someone more in sync with Democratic politics in charge.

If Mr. Powell isn’t given a new four-year term next February, when his current term expires, the leading contender for the job is Fed governor Lael Brainard, an economist appointed to the board in 2014 by former President Barack Obama.

Ms. Warren stopped short of endorsing Ms. Brainard in a recent television interview but singled out her record of dissents on regulatory matters under Mr. Powell. “She makes a good case for why it is the job of the Federal Reserve to be that cop on that beat,” Ms. Warren said in an Aug. 4 interview on Bloomberg TV.

Critics of Mr. Powell have reached out to Democratic Sen. Elizabeth Warren in recent weeks to press the case that the White House should seek new Fed leadership.

Photo: Tom Brenner/Bloomberg News

Senate Banking Committee Chairman Sherrod Brown (D., Ohio) is also among those who have said the Fed should adopt a more muscular regulatory approach.

Critics of Mr. Powell, including former Senate Democratic policy aides, have reached out to Ms. Warren, Mr. Brown and other influential advocates in recent weeks to press the case that the White House should seek new Fed leadership.

Some inside the administration see reappointing Mr. Powell as the safest option given a host of vexing economic issues right now, including coming votes on an infrastructure spending bill, higher-than-expected inflation and rising Covid-19 cases from the Delta variant, according to people familiar with deliberations. But the situation remains fluid in part because several senior White House advisers haven’t yet focused on the decision over who should lead the Fed.

A White House official said Mr. Biden will appoint the candidates who he thinks will be the most effective in implementing monetary policy.

Treasury Secretary and former Fed Chairwoman Janet Yellen has said publicly that the Fed has done a good job under Mr. Powell. Her influence in the final selection remains a question mark. At least one personnel pick favored by Ms. Yellen was scrapped after facing opposition from progressives.

Ms. Warren played a key role eight years ago in rallying opposition against the Obama administration’s potential nomination of former Treasury Secretary Lawrence Summers to become Fed chairman. Opposition from Democratic senators led Mr. Summers to withdraw from consideration, paving the way for Mr. Obama to nominate Ms. Yellen.

The current situation is different because Mr. Powell, a Republican who was nominated to the Fed board as a governor in 2011 by Mr. Obama and tapped to become chairman in 2017 by Mr. Trump, is generally well-liked by lawmakers from both parties. Analysts believe he is likely to draw enough support from Republicans and Democrats to win confirmation by a comfortable margin. Mr. Powell won support from 84 senators during his Senate confirmation in 2018; 68 of those senators remain in office, equally split between the party caucuses.

But opposition from Ms. Warren and other progressive critics of the Biden administration could force an intraparty fight. Ms. Warren in 2013 effectively blocked the planned nomination of Treasury Department official Antonio Weiss, though he went on to serve in a similar capacity as a department adviser.

Federal Reserve Board Governor Lael Brainard’s record of dissents on regulatory matters under Mr. Powell was recently praised by Ms. Warren.

Photo: brian snyder/Reuters

Mr. Powell and Ms. Brainard have had similar views on monetary policy in recent years, but Ms. Brainard has in recent months argued more forcefully for the Fed to develop a central bank digital currency. Mr. Powell has said he is undecided on whether the risks outweigh the benefits. Ms. Warren has also recently talked up the potential benefits of such a project.

Mr. Biden passed over Ms. Warren for the post of Treasury secretary but has stocked his administration with her former staffers and other favorites, and her backing has been an important credential for other financial regulatory posts.

Earlier this year, progressive opposition, including from Mr. Brown, prompted the White House to scrap plans to nominate Michael Barr, a former Obama administration Treasury official, as a top banking regulator.

Reappointing Mr. Powell “would be disappointing” for those who care about Mr. Biden’s agenda to address financial regulation, climate change and racial wealth gaps, said Erik Gerding, a senior fellow at Americans for Financial Reform, a nonprofit that argues for tougher financial regulation. “Having Jerome Powell continue would just mean one less vote for sustained and healthy regulation of the banking system.”

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Mr. Powell’s record has won him enthusiastic support from other Democrats. “It’d be fine with me if President Biden named him Fed chair for life,” said Denny Heck, a Democrat who served eight years on the House committee that oversees the Fed. He left in January, when he became lieutenant governor of Washington state.

The Biden administration also has been working on filling a vacancy on the seven-member Fed board of governors. The two leading contenders for that job are Williams Spriggs, chief economist at the AFL-CIO, and Lisa Cook, an economics professor at Michigan State University.

Mr. Spriggs is seen for now as the more likely selection, according to people familiar with the matter. Mr. Spriggs served from 2009 to 2012 as assistant secretary for policy at the Labor Department and is also a professor of economics at Howard University.

The decisions about whom to appoint to two other top Fed board posts are tied to the chairman selection, according to people familiar with the matter. If Mr. Powell gets a second term, Ms. Brainard is likely to be asked to serve as the vice chairwoman or as the vice chairwoman for bank supervision.

Richard Clarida’s current term as vice chairman expires in January. Another candidate being considered for the job is Seth Carpenter, an economist who spent 15 years at the Fed, most recently as deputy director of the monetary affairs division.

Mr. Carpenter worked at the Treasury Department from 2013 until 2016. He was nominated in August 2014 to be assistant secretary for financial markets; he filled the position on an acting basis, but his nomination wasn’t ever considered by the Senate. He became global chief economist at Morgan Stanley last month after serving in a similar capacity at UBS Group AG .

The four-year term of vice chairman of bank supervision, currently held by Randal Quarles, expires in October. Mr. Quarles has said he is likely to remain on the board as a governor at least until his term leading a separate international body, the Financial Stability Board, expires at year’s end.

Administration officials are considering former Fed governor Sarah Bloom Raskin as a possible candidate for that job. Ms. Raskin, a lawyer, served as deputy Treasury secretary in the Obama administration from 2014 to 2017. She was critical last year of some of the Fed’s emergency lending programs and argued officials should have done more to prevent broad market backstops from benefiting certain energy companies.

Even though Mr. Powell and Ms. Brainard have been aligned on monetary policy, the selection could make a “meaningful difference,” said James Sweeney, chief economist at Credit Suisse Group AG . “Brainard is seen to be closer to her party than Powell is to his. The politics of Brainard may be a little trickier in the long term…. It would be a more-charged political environment for the Fed.”

Write to Nick Timiraos at nick.timiraos@wsj.com