BP’s trial in connection with the 2010 Deepwater Horizon oil spill began today in New Orleans, and there are hints that a deal could be near.

The oil giant said last week it was gearing up to launch a defense against the hefty fine it could face under the Clean Water Act.

BP

The New York Times reports that the deal currently being discussed among BP plc (NYSE:BP) (LON:BP) and federal and state authorities could be worth about $16 billion, and it would limit the size of the fine BP would pay under the Clean Water Act. It could also help the company reduce its tax liability.

Under the possible deal, BP plc would pay $9 billion for the damages to the natural resources in the Gulf of Mexico and for restoration efforts.

The company would pay just $6 billion in fines under the Clean Water Act, and $1 billion would go into a special fund in case additional damages to the environment begin to develop as a result of the massive oil spill.

This proposal could be attractive to BP because of the small amount it would pay under the Clean Water Act. The company could have been saddled with $13 billion to $21 billion in fines under that law alone, in addition to the fines it must pay for damages and restoration.

According to The New York Times, none of the parties involved have commented on any proposals, although several lawyers have told the newspaper that the $16 billion proposal has been made. That proposal also provides a basic plan for the division of settlement cash among the states affected by the oil spill.

If BP accepts the proposal, it would also limit its tax liability because the amount BP must pay would be levied mostly as penalties rather than fines. Penalties, like those assessed for damage and restoration costs, are tax-deductible, however the fine assessed under the Clean Water Act would not be.

Shares of BP plc (NYSE:BP) (LON:BP) fell 2 percent at the New York Stock Exchange.