The Journal said the final settlement amount could be less than $10 billion. Still, the multibillion dollar figure would put the fine among the largest penalties imposed on a bank and is far higher than what BNP has provisioned for.
Overall, the bank has set aside around 2.7 billion euros ($3.68 billion) for litigation-related costs.
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BNP Paribas and the Justice Department declined to comment.
The $10 billion settlement figure would represent a "hit" of around 5 percent to the bank's tangible book value, Citigroup analysts said in a research note.
It would also reduce BNP Paribas' common equity tier 1 capital ratio to around 9.5 percent, a hit of around 10 percent on the bank's reported tier 1 capital ratio for the first quarter of 2014, Citigroup analysts said.
A settlement of this magnitude would also result in a 5 euro per share impact on the fair value of BNP Paribas stock, Citigroup said.
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Prosecutors have also pushed the bank to plead guilty to criminal charges as part of a resolution, sources have previously said.
The Journal said limited fallout of a guilty plea earlier this month by Credit Suisse Group has further emboldened prosecutors. Credit Suisse pleaded guilty to a U.S. criminal charge and agreed to pay more than $2.5 billion in penalties for helping Americans evade taxes.
In early May, BNP Paribas Chief Executive Officer Jean-Laurent Bonnafe and the bank's lawyers met with the New York Department of Financial Services, one of the authorities involved in the probe, and made a plea for leniency, one source said earlier this month.
The source said the regulator, led by Benjamin Lawsky, would not revoke the bank's license if other stiff penalties were included in the settlement. Such penalties, however, could include temporarily suspending dollar clearing through New York and terminating more than a dozen employees.
The bank has expressed concerns about the prospect of such a suspension, telling authorities that its inability to clear dollar transactions could destabilize it, the Journal reported.
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North America is a key part of BNP's new strategy to increase profits outside Europe. It aims for the region to account for 12 percent of its 2016 revenues, up from 10 percent in 2013.
A final resolution of the BNP Paribas investigation is likely weeks away, the Journal said on Thursday