The lender is in negotiations with regulators including the New York Department of Financial Services (DFS) and has set aside $1.1bn to cover the bill – but has also warned the sum could be considerably higher.
Sources close to the negotiations told Bloomberg that the bill could come to $5bn, with strings attached such as limiting the bank’s right to transfer US dollars internationally.
But credit ratings agency Fitch expects the settlement to be based on that of Credit Suisse earlier this week, which Fitch believes could set a precedent for similar cases.
The Swiss bank pleaded guilty to helping clients evade taxes and paid a $2.5bn fine, but did not have any licences revoked.
BNP Paribas and the DFS declined to comment.
Its shares ended the day down 1.32 per cent.