REUTERS/Shannon Stapleton
The settlements would fault the bank for turning a blind eye to Madoff's huge Ponzi scheme, the Times said, citing people briefed on the case.
JPMorgan spokesman Joseph Evangelisti declined to comment on the New York Times report when contacted by Reuters.
Madoff was convicted in 2009 of defrauding thousands of investors and is serving a 150-year prison sentence. JPMorgan has been accused of ignoring warning signs that Madoff's business was a fraud, often to win more fees and commissions for services they provided.
The New York Times said the settlement with federal prosecutors in Manhattan would include a so-called deferred-prosecution agreement and more than $1 billion in penalties to resolve the criminal case.
The rest of the fines would be imposed by Washington regulators investigating broader gaps in the bank's money-laundering safeguards, the paper said.
JPMorgan, the biggest U.S. bank by assets, recently reached a $13 billion settlement of a range of government claims over bad mortgage securities and struck another deal with regulators to pay about $1 billion for its "LondonWhale" derivatives trading debacle.
(Reporting by Chris Peters in Bangalore; Editing by Supriya Kurane)