The two officials asked to remain anonymous because they were not authorized to speak publicly about the deal.
Talks have been dragging on for more than a year between major U.S. banks and state attorneys general over fraudulent foreclosure practices that drove millions of Americans from their homes during the housing crisis.
In October 2010, major banks temporarily suspended foreclosures following revelations of widespread deceptive foreclosure practices by banks. That has backlogged millions of foreclosures that must be cleared before the housing market can fully recover.
The settlement would only apply to privately held mortgages, not those held by government-controlled Fannie Mae or Freddie Mac. Fannie and Freddie own about half of all U.S. mortgages, roughly about 31 million U.S. home loans.
Individual states can opt out of the proposed deal. Some have disagreed over what terms to offer the banks.
In September, California announced it would not agree to a settlement over foreclosure abuses that state and federal officials have been working on for more than a year.
New York, Delaware, Nevada and Massachusetts, which sued five major banks earlier in December over deceptive foreclosure practices, have also argued that banks should not be protected from future civil liability.
And both sides have also fought over the amounts of money that should be placed in the reserve account for property owners who were improperly foreclosed upon. Many of the details of the deal, including a $25 billion cost for the banks, have been agreed upon, officials say.