The trial resulting from the 2010 explosion of a Gulf of Mexico drilling rig began Monday morning.
The possible $16 billion settlement would limit Clean Water Act fines paid by BP to $6 billion, a source briefed on the deal told the Times.
In addition, BP would pay $9 billion to cover damages to natural resources and restoration, and another $1 billion would be put in a fund to offset unanticipated environmental damages related to the spill developed.
The Times said officials at BP, the Justice Department or the states commented on any settlement, but several lawyers briefed on the negotiations said a $16 billion settlement proposal had been offered.
States that would be affected by any settlement are Alabama, Florida, Louisiana, Mississippi and Texas, though only Alabama and Louisiana are participating in the trial, the Times said.
Meanwhile, Alabama Attorney General Luther Strange said in his opening statement BP's actions concerning the gulf spill were driven by greed.
"At BP, money mattered most," Strange said.
Saying the spill was predictable and preventable, Strange said the oil giant's "culture of callousness" caused it to happen.
"Money mattered more to BP than the gulf. A lot more," Strange said. "Your honor, the evidence will be clear and unmistakable: Greed devastated the gulf."
BP should be slapped with the highest possible civil fine and a ruling of gross negligence not preventing the Deepwater Horizon catastrophe, Louisiana Attorney General Buddy Caldwell.
Caldwell said during his opening statement Monday in federal court in New Orleans evidence will show "willful and wanton misconduct" by BP in the April 2010 fire and explosion on the rig that killed 11 workers and spewed 200 million gallons of crude oil into the Gulf of Mexico, AlabamaLive.com reported.
"Punitive damages should be the highest allowed by law," Caldwell said.
Louisiana still is suffering damages because of the spill that lasted 87 days.
"This is a continuing tragedy to this very day," he said, noting that more than 1 million barrels of oil are unaccounted-for in the gulf.
Brad Brian, representing Transocean, said the company and the rig's crew were victims of BP's negligence. Mistakes were made, he said, but they weren't intentional.
"The Transocean crew did their duty. They died doing their duty," Brian said. "They died, not because they weren't trained properly, but because critical information was withheld from them.
Jim Roy, representing the Plaintiffs Steering Committee, began the day's comments with attacks on Transocean, which owned the Deepwater Horizon rig, and BP. Roy, a Louisiana trial lawyer, said evidence will show BP guilty of gross negligence.
BP "had a we-can-get-away-with-this attitude," Roy said. "They put profits over safety, again and again."
U.S. District Judge Carl Barbier said he expected the initial phase of the trial to last three months.
In late January, BP pleaded guilty to criminal environmental charges, agreeing to pay $4 billion to settle the charges.