With the Federal Reserve trying to orchestrate a sustained recovery that will restore jobs lost during the Covid-19 pandemic without igniting inflation, Biden's decision could have lasting consequences.
Progressive Democrats have called on Biden to oust Powell, a Republican, and name a comparatively liberal candidate who will do more to tighten oversight of banks and address climate change and systemic racism.
But failing to name the Fed chief to a second four-year term could jar financial markets and open Biden to charges of playing politics with the independent system.
The White House has not said when Biden will make a decision, but it is likely to be soon, since the terms of two other top roles at the institution will end in in coming weeks.
Powell took the reins of the central bank in early February 2018, tapped by then-president Donald Trump, who bucked tradition and ousted Janet Yellen -- the first woman to serve in the role -- after just one term.
But Powell has since won praise for his ability to bridge divergent opinions on the Fed's policy-setting committee, and for acting quickly when the pandemic struck to slash interest rates to zero and pump trillions of dollars into the financial system.
Those actions, along with further trillions in government spending, helped avert a worse downturn, and the world's largest economy has recovered to its pre-pandemic size.
Powell repeatedly stresses the need to sustain growth to ensure the economy benefits marginalized Americans, and supports a cautious approach to removing the Fed's pandemic stimulus.
While unemployment fell to 5.2 percent in August, there are still five million jobs lost to the Covid-19 crisis that have not returned.
But the progressive wing of the Democratic party, including outspoken representatives Alexandria Ocasio-Cortez, Rashida Tlaib and Ayanna Pressley, want the central bank to venture into areas beyond its dual mandate of stable prices and full employment, such as the fight against climate change.
"To move forward with a whole of government approach that eliminates climate risk while making our financial system safer, we need a Chair who is committed to these objectives. We urge the Biden Administration to use this opportunity to appoint a new Federal Reserve Chair," they said in a statement last week.
Other progressive groups have joined the call for a new leader, saying the Fed can do more to address racism and prevent the rollback of banking regulations implemented in the wake of the 2008 global financial crisis.
However John Yarmuth, Democratic chair of the House Budget Committee, supports a second term for Powell.
"Chair Powell has led the Federal Reserve with a steady hand through a time of severe crisis in our nation," he said in a statement last week.
"As our nation and economy continue to face uncertainty, a consistent and focused Federal Reserve is critical."
Democratic Senator John Tester, a centrist who leads the Senate Banking Committee, warned against politicizing the decision.
"They should not be involved in the political footballs thrown around on Capitol Hill," Tester told The Wall Street Journal on Wednesday. "That's the reason I want Jerome Powell. He's proven he can maintain the independence of the Fed."
The Fed chief also appears to have a key endorsement: his predecessor and current Treasury Secretary Janet Yellen, according to a Bloomberg report.
One potential compromise option would be for Biden to retain Powell but appoint more liberal officials to the four-year terms of Fed vice chair and vice chair of banking supervision.
The terms of those roles' current occupants expire in mid-September and mid-October, respectively. Biden could also appoint a progressive to a vacancy on the Fed board.