NEW ORLEANS — As settlement talks continued Sunday on the eve of a trial against BP stemming from the 2010 explosion of a drilling rig in the Gulf of Mexico, the details of an offer by federal and state officials to the oil company started to emerge.

The plan, worth a total of $16 billion, would limit the fines paid by BP under the Clean Water Act to $6 billion, a proposal that could help reduce its tax liability, said one person briefed on the plan who spoke on the condition of anonymity.