Volcker, who served as Federal Reserve chairman under Presidents Carter and Reagan, is often credited with combating high inflation during the 1980s. In the recent crisis, he became famous for promoting what became known as the Volcker Rule, which puts limits on proprietary trading by U.S. banks.
Volcker advocated barring lenders from committing their own funds to speculative investments, such as private-equity investments to mortgage-backed securities and other sophisticated bets. He believes that kind of speculative activity was partly responsible for causing the financial crisis. Wall Street banks largely disagreed, and opposed the Volcker Rule. In the end, a much softer version was included in the 2010 financial reform bill.
The Associated Press first broke the story, and other media outlets have been told the same by their sources. A formal announcement is expected Friday.
Volcker's departure follows the resignation by Lawrence Summers as Obama's chief economic adviser in September. Obama is likely to announce who will be taking over as director of the National Economic Council on Friday.