The bank will also, unusually, admit guilt, Financial Times and The New York Times reported.
According to the Wall Street Journal, BNP plans to slash its dividends and issue billions of euros of bonds to pay the fine.
The bank is accused of breaking sanctions against Iran, Sudan and Cuba.
This is alleged to have taken place between 2002 and 2009.
The reported size of the fine could almost wipe out BNP’s entire 2013 pre-tax income of about $11.2 billion.
In April, BNP Paribas said it had set aside $1.1 billion to cover the cost of US penalties, but warned that the “amount of the fines could be far in excess of the amount of the provision”.
Earlier this month, one of the EU’s top officials intervened in the controversy.
Michel Barnier, the EU’s internal markets commissioner, said any penalty on the giant French bank must be “fair and objective”. Reports at the time suggested the fine would be in the region of $10 billion.
France’s President Francois Hollande has raised the matter with President Barack Obama, while French Foreign Minister Laurent Fabius recently warned that such a fine could hurt EU-US trade treaty talks.
As part of the deal with US authorities, BNP may be suspended from converting foreign currencies into dollars, reports suggest, which would hit its ability to operate in international wholesale banking markets.
US authorities are keen to make an announcement on the settlement on Monday afternoon.
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