In the latest talks, the industry offered to pay about $196 billion to resolve the remaining state lawsuits, officials familiar with the terms said.
Such state lawsuits are of greatest concern to tobacco producers.
It began with the state lawsuits against tobacco companies, which accelerated the national battle over smoking.
The Minnesota suit was the first of the more than three dozen state lawsuits against the tobacco industry to go to trial.
The state lawsuits were based on novel legal theories.
It will be the first of many such state lawsuits, they say.
That deal, if approved by Congress, would resolve all existing state lawsuits.
However, the industry had feared the state lawsuits more than the private claims because they had the power of government behind them.
None of the state lawsuits have ever been resolved by a jury.
The state lawsuits represent the major regulatory and financial threat they face.