The upper end of the range matches the amount Morgan Stanley agreed to pay in February to resolve the FHFA's claims against it. The person familiar with the matter said the negotiations are still ongoing, and the final amount of any deal remains fluid. The person was not authorized to speak publicly on the matter.
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The Wall Street Journal first reported the settlement talks.
The FHFA has recovered $16.1 billion in agreements with other banks. Goldman is among four banks still facing FHFA mortgage-related lawsuits, along with HSBC Holdings, Nomura Holdings and Royal Bank of Scotland Group.
On Wednesday, Goldman, HSBC and Nomura argued that U.S. District Judge Denise Cote in New York, who is overseeing the litigation, should reconsider her decision that the agency did not wait too long in suing the banks.
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The renewed bid to dismiss the lawsuits based on timeliness issues stemmed from a June ruling from the U.S. Supreme Court. The court ruled in an environmental case that a federal law did not preempt a state-law statute that placed time limits on bringing a lawsuit that applied even if a plaintiff did not know it had a claim.