An insider told Bloomberg that her name was put forward for the role by Christopher Dodd, the chairman of the Senate Banking Committee.
The Bureau of Consumer Financial Protection is being established as an independent body within the Federal Reserve and is designed to regulate against mortgage lending and credit card abuses by banks.
Ms Bair was one of the front runners for the top job at the agency due to her experience of running the FDIC, as well as her bipartisan appeal.
It is now thought President Barack Obama will turn to either assistant Treasury secretary Michael Barr or Harvard law professor Elizabeth Warren when deciding on the bureau's new leader.
Last month, Ms Bair warned that some global regulators are being persuaded by "disingenuous" banking lobbyists that a softer stance to international capital standards is needed to sustain the recovery, reported the Financial Times.
By Gary Cooper