Yellen, 74, would be the first woman to assume the position if confirmed by the Senate.
She was also the first woman to chair the Federal Reserve (the Fed) and the White House Council of Economic Advisers.
The labor economist will lead the Biden administration's efforts to recover the economy after it was paralyzed by the global coronavirus pandemic.
Yellen was confirmed as the Fed chair by the Senate in 2014 with a 56-26 vote. After serving a four-year term, she was not re-nominated by U.S. President Donald Trump.
The report came hours after Biden announced several key picks for foreign policy and national security.
Biden named Antony Blinken as secretary of state, Alejandro Mayorkas as secretary of Homeland Security (DHS) and Avril Haines as director of National Intelligence.
While Linda Thomas-Greenfield is set to be the new U.S. ambassador to the U.N., Jake Sullivan is nominated as a national security advisor and John Kerry was picked for the special presidential envoy for climate position.