The group said it was in discussions with the United States Department of Justice (DoJ) and the Securities and Exchange Commission (SEC) over settling all criminal and SEC claims against BP related to the Gulf of Mexico oil spill in 2010.
BP said “no final agreements have yet been reached” and any deal would be subject to US court approvals.
But reports suggest BP is poised to plead guilty to criminal misconduct in exchange for a waiver of future prosecution on the charges.
It is thought the deal could see it pay a record penalty, surpassing even the 1.3 billion US dollar (£820 million) fine paid by drugs group Pfizer in 2009 for marketing fraud related to a pain medicine.
The Deepwater Horizon blast in April 2010 killed 11 workers and led to the worst offshore oil spill in US history.
BP has struggled to shake off the reputational blow of the explosion, despite paying out billions of dollars so far to cover costs and claims.
The group said current settlement discussions - which could see a deal announced as early as today - are not expected to cover civil claims, including damages under the Clean Water Act, federal and state Natural Resource Damages claims or outstanding private civil claims.
The group has been selling assets as part of its pledge to raise cash to pay the costs of the Gulf of Mexico disaster.
It has recently sold a Texas City refinery, five oil and gas fields in the US Gulf of Mexico and its Bristol-based liquefied petroleum gas (LPG) distribution arm.
BP has announced disposals since the start of 2010 for a total of more than 35 billion US dollars (£22 billion) against its target of 38 billion US dollars (£24 billion), excluding the proposed deal with Rosneft for the sale of BP’s 50% share in Russian joint venture TNK-BP.
Aside from legal claims, BP expects to make a final payment of 860 million US dollars (£543 million) into the 20 billion US dollar (£12.6 billion) Gulf of Mexico Trust Fund by the end of the year.