Purdue Pharma, the opioid drug-maker owned by the billionaire Sackler family, is reported to be offering between $10bn and $12bn to settle thousands of lawsuits against it.
The firm is facing over 2,000 lawsuits linked to its painkiller OxyContin.
Purdue told the BBC it was "actively working" towards a "global resolution" but would not comment on the amount.
NBC, which first reported the news, said the settlement would involve the Sacklers giving up ownership of Purdue.
The firm said in a statement: "While Purdue Pharma is prepared to defend itself vigorously in the opioid litigation, the company has made clear that it sees little good coming from years of wasteful litigation and appeals.
"Purdue believes a constructive global resolution is the best path forward, and the company is actively working with the state attorneys general and other plaintiffs to achieve this outcome."
According to Reuters, there is currently no agreement and the settlement discussions could collapse.
What is the opioid crisis?
Opioids are a group of drugs that range from codeine, to illegal drugs like heroin.
Prescription opioids are primarily used for pain relief. They can be highly addictive.
On average, 130 Americans die from an opioid overdose every day, according to the US Center for Disease Control and Prevention.
Opioids were involved in almost 400,000 overdose deaths in the US from 1999 to 2017, according to its research.
Purdue is one of 22 opioid makers, distributors and pharmacies named in over 2,000 cases which are due to go to trial in October.
The cases, which have been brought by states, cities and counties, allege the company used deceptive practices to sell opioids and is responsible for fuelling an opioid addiction crisis in the US.
Purdue has said that the US regulator, the Food and Drug Administration, approved labels for OxyContin that had warnings about the risks.
Oklahoma ruling against Johnson & Johnson
On Monday, drugmaker Johnson & Johnson was ordered by a US judge to pay $572m (£468m) for its part in fuelling Oklahoma's opioid addiction crisis.
The state's lawyers say some 6,000 people there had died from opioid overdoses since 2000.
They accused Johnson & Johnson of carrying out a years-long marketing campaign that minimised the addictive painkillers' risks and promoted their benefits.
The company vigorously denied any wrongdoing and said immediately after the judgement that it would appeal.
Earlier this year, Oklahoma settled with Purdue Pharma for $270m and Teva Pharmaceutical for $85m.
Who are the Sackler family?
Brothers Arthur, Mortimer, and Raymond Sackler were all doctors from Brooklyn, New York. In the early 1950s they bought a medicine company called Purdue Frederick which would become Purdue Pharma.
Much of their fortune comes from Purdue Pharma.
The Sacklers are prolific philanthropists, and their name adorns a wing of the Louvre in Paris, in the Metropolitan Museum of Art in New York as well as the V&A, the Serpentine and Shakespeare's Globe in London among many, many others.
As the opioid scandal has engulfed the Sacklers, a number of high-profile museums - including the Tate in the UK - have announced they will no longer take money from the family.
The Sacklers have argued they were passive board members of Purdue Pharma, who approved routine management requests and were not involved with the marketing of OxyContin.