Citing people familiar with the discussions, The Wall Street Journal said late Friday that the settlement would cover fines BP owes under the Clean Water Act, a federal water pollution law, as well as payments under the Natural Resources Damage Assessment, an environmental evaluation.
But the Journal noted that it remained unclear whether the government had formally proposed the offer to BP.
The April 20, 2010 explosion on the Deepwater Horizon oil rig, operated by BP off New Orleans, killed 11 people and spilled hundreds of millions of gallons of crude oil into the Gulf of Mexico in the four months it took to cap the well.
BP vowed Tuesday to "vigorously defend" itself in court against what it termed "excessive" fines for the incident. The company already pleaded guilty, in November, to criminal charges -- including felony manslaughter - and agreed to pay a record $4.5 billion in criminal fines.
It reached a $7.8 billion settlement early last year to cover the bulk of the outstanding private claims for economic loss, property damage and medical problems.
BP has paid out $10 billion to businesses, individuals and local governments impacted by the spill and spent more than $14 billion on the response and cleanup.
The oil firm also remains on the hook for billions in additional damages, including the cost of environmental rehabilitation.