Sheila Bair, former chairwoman of the Federal Deposit Insurance Corp. (FDIC), is the leading candidate to monitor banks during a nationwide foreclosure settlement, according to Bloomberg News.

The position would have access to foreclosure records and the ability to audit servicers, which could lead to penalties for banks that didn't meet performance measures and timelines. The banks include JPMorgan Chase, Wells Fargo, Ally Financial, Citigroup and Bank of America.

Major banks, U.S. states and federal officials must agree to the selection, one of the final details to be decided in the foreclosure investigation.

All 50 states began investigating bank foreclosure actions after revelations of "robosigning" and irregular paperwork. The framework of the deal could total $25 billion for the five largest banks, and an agreement could be reached by Christmas, sources told Bloomberg.

Bair, currently a senior adviser to Pew Charitable Trusts, reportedly turned down the position two months ago because she was working on a book.

Update: Bair denied that she would be overseeing the foreclosure settling on a Monday appearance on CNN. "I'm not in a position to do that," she said.

She was appointed as chairwoman of the FDIC in June 2006 by President George W. Bush, rising to prominence during the financial crisis of 2008. Bair pushed for the FDIC to gain authority under the Dodd-Frank bill to unwind bankrupt companies.

Earlier this month, the Massachusetts attorney general filed a suit against the five major lenders, pre-empting the nationwide settlement. As a result, Ally Financial's subsidiary, GMAC Mortgage, said it would soon be suspending its operations in the state.

Banks are also involved in litigation with federal regulators over mortgage-backed securities that were guaranteed by Fannie Mae and Freddie Mac prior to the subprime crisis.