With a major civil trial scheduled to start Monday in New Orleans against BP over damages related to the explosion of an offshore drilling rig in 2010, federal officials and those from the five affected Gulf Coast states are trying to pull together to strike an 11th-hour settlement in the case.

A lawyer briefed on those talks said that the Justice Department and the five states — Alabama, Florida, Louisiana, Mississippi and Texas — had reportedly prepared an offer to resolve the two biggest issues central to a series of trials against BP, the first of which starts Monday.

One of those issues is the fines that the company would pay for violations of the Clean Water Act related to the four million barrels of oil spilled after the explosion of the Deepwater Horizon rig, which BP had leased from Transocean. The other point of dispute is how much the company will have to pay in penalties under a different environmental statute for damage caused by the oil to the area: beaches, marshes, wildlife and fisheries.

The Wall Street Journal reported late Friday that federal and state officials were preparing a $16 billion settlement offer that would cover both the Clean Water Act fines and environmental penalties related to the spill. “The ball is on BP’s side of the table,” said the lawyer, who spoke on the condition of anonymity because he was not authorized to speak publicly on the matter.