A settlement could cost as much as $1.4 billion, the Journal reported Thursday.
Added to a $616 million fine the firm agreed to pay in March, SAC would likely be paying around $2 billion.
Lawyers from the Securities and Exchange Commission and the hedge fund are negotiating the sum and other details, such as how long to ban the fund's founder Steven Cohen from managing money for other investors, sources said.
The firm has denied any wrongdoing, but 11 former employees have been implicated in the insider trading case with six of them pleading guilty and two trials set to begin soon.
All told, prosecutors in Manhattan have charged 89 people with insider trading since August 2009 and 75 have been convicted or pleaded guilty, the Journal reported.
The settlement with SAC does not end a separate investigation into Cohen's behavior that has yet to result in charges.