The deal could be announced as early as Tuesday in New York, officials told the Journal.
Citing people familiar with the matter, the Journal said that the figure includes nearly $1.3 billion, a record amount for a bank, as part of a deferred prosecution agreement.
The London-based bank also would pay a civil fine of more than $650 million, according to people briefed on the issue, the newspaper said.
US lawmakers have accused the global bank of giving Iran, terrorists and drug dealers access to the US financial system.
Criminal investigators have been pursuing some of the same allegations highlighted in the Senate probe, the Journal noted.
HSBC in July admitted to poor anti-laundering controls.
The settlement would resolve investigations by the Justice and Treasury departments and other federal agencies, as well as the Manhattan district attorney.
As part of the HSBC settlement deal, the Journal said, citing a government official, it will admit to violating the Bank Secrecy Act and the Trading with the Enemy Act.
The US Treasury declined to comment on the Journal report.
In early November HSBC said it had increased the amount set aside for fines linked to money-laundering in the United States to $1.5 billion.
The Journal report came the same day the US Treasury announced that another British bank, Standard Chartered, would pay $327 million to settle charges it violated US sanctions on Iran, Myanmar, Libya and Sudan.
For Standard Chartered, the fines from the Treasury and other US federal and local regulators brought to $667 million the total it has been charged for sanctions violations.
