The employees authorities plan to arrest are former bank manager Javier Martin-Artajo, who reportedly instructed a trader, Julien Grout, to undervalue losses that eventually totaled about $6 billion, the Times said.
Lawyers for the two former employees could not be reached or declined to comment about the case. The FBI, the U.S. attorney's office in Manhattan and a bank spokesman declined to comment on the case, the Times said.
The losses derived from huge bets on derivatives made by traders in JPMorgan's London office.
Derivatives are financial products with values that are tied to an underlying asset, such as a corporate bond.
Because the value of the losses was minimized, the bank in July, reported that its first quarter losses in 2012 were $459 million more than originally stated in that quarter's financial report.
The losses were first reported in May 2012. Soon thereafter, the media seized on the possibility that a trader nicknamed "the London Whale," whose real name is Bruno Iksil, was behind the losses through his reckless trading.
But Iksil has since signed cooperation agreements with authorities, the Times reported.
He may face some charges, but the case has turned in the media from a rogue-trader type of case to one that is focused on flaws in the risk-containment practices at the bank.
Britain's Financial Conduct Authority is also planning to fine the bank, a source close to the case told the Times.
The U.S. Securities and Exchange Commission is using the case to exemplify its new policy of seeking guilty convictions or admissions from financial firms that have traditionally been allowed to pay a fine with out admitting or denying any wrongdoing.
The agency has been criticized for being soft on firms that contributed to the financial crisis, which, in turn, lead to a nearly global economic downturn and the loss of millions of U.S. jobs.
The SEC has long held to the belief that not forcing an admission of guilt on a financial firm offers a chance for much faster compensation to bank fraud victims.
But derivatives are complex financial instruments not clearly understood even by professionals, let alone by juries. There is also considerable leeway in estimating their value, which could make it hard to prove that Martin-Artajo and Grout deliberately tried to mislead anyone, the Times said.
How inaccurate is a valuation estimate allowed to be? Iksil, in a taped phone call once said that the estimated losses were "getting idiotic."
"I can't keep this going," Iksil said.