Bank representatives and government officials are pushing to put the finishing touches on a broad settlement of most state and federal investigations of alleged foreclosure improprieties that could force five large banks to make concessions worth roughly $19 billion.

Housing and Urban Development Secretary Shaun Donovan and state officials hope to reach a deal as soon as this week, though any agreement could be delayed by unresolved issues including the naming of a monitor to oversee the agreement.

The settlement would end months-long negotiations among federal officials, state attorneys general and the nation's five largest mortgage banks: Ally Financial Inc., Bank of America Corp., Citigroup Inc., JPMorgan Chase & Co. and Wells Fargo & Co. The talks center on the banks' use of "robo-signing," in which employees approved legal documents without proper review, and other questionable foreclosure practices. Representatives of the five banks declined to comment.

The value of the settlement could be as large as $25 billion if it includes California, which left the talks in September. California accounted for 13.1% of all mortgages outstanding at the end of September and 10.8% of all loans in foreclosure, according to the Mortgage Bankers Association. Without California, the value of the deal is likely to be roughly $19 billion, people familiar with the talks said. A spokesman for California Attorney General Kamala D. Harris declined to comment.

The dollar value of the deal would include the value of principal write-downs, interest-rate reductions and other benefits to homeowners as well as cash penalties.

The Obama administration has been pushing for a 50-state deal, but its efforts have run into opposition from labor unions and liberal groups that have warned that the proposed settlement is inadequate. Previous efforts by the administration to deal with the foreclosure crisis have been criticized as falling short of expectations.

It isn't clear how many states will agree to a settlement. Besides California, attorneys general in Arizona, Delaware, Massachusetts and New York also have expressed reservations about a potential deal. New York Attorney General Eric Schneiderman has had several conversations with Mr. Donovan in recent months, people familiar with the matter said.

"We remain engaged with our federal counterparts to ensure there is real accountability for misconduct in the mortgage industry and significant relief for those who have suffered through this crisis," a spokesman for Mr. Schneiderman said.

Administration officials have viewed the foreclosure settlement as a chance to break the foreclosure logjam, increase the number of reductions in loan principal and provide other assistance to homeowners. Banks, meanwhile, would like to reassure investors and put questions related to foreclosure practices behind them.

But several issues remain. The two sides still must choose a monitor who will be responsible for seeing that banks comply with the agreement; they also still are working on a mechanism under which states can act to enforce the settlement.

Among those being considered for the monitor position is North Carolina Commissioner of Banks Joseph A. Smith Jr. A spokeswoman for Mr. Smith said he was unavailable for comment.

Former Federal Deposit Insurance Corp. Chairman Sheila Bair was approached a few months ago about the job, but said she wasn't interested because of other commitments, according to a person familiar with the situation. She won't reconsider, this person said.

Negotiators still are ironing out details to determine what additional legal claims prosecutors could bring once a deal is signed. Under the proposal, banks would be released from legal claims tied to servicing delinquent mortgages as well as certain mortgage-origination practices, but government officials still would be able to pursue claims related to the packaging of mortgages into securities.

Even if a deal in principle is reached, the formal announcement of the agreement could be delayed until January. Once a deal is agreed to, it is likely to take a month or two for the legal language to be finalized, people familiar with the discussions said.

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