The False Claims Act suit, which remains under seal, alleges that Armstrong defrauded the U.S. government based on his years of denying use of performance-enhancing drugs, said the people, who asked not to be identified because the government hasn't made its plans public yet.
"Typically when the government joins the case it is resolved in a way that results in a recovery for the government," John Phillips of Phillips & Cohen in Washington, who has litigated whistleblower cases since 1986, said in an interview.
He said the government only joins about 25% of cases filed under the False Claims Act.
The Justice Department recovered a record $3.3 billion in suits filed by whistleblowers in the 2012 fiscal year, the department said in December. When the government chooses to intervene and wins a False Claims case, the whistleblower can receive from 15 percent to 25 percent of the recovery.
The U.S. Postal Service paid about $40 million under its contract with Tailwind Sports, which owned the team Armstrong rode with, from 1996 to 2004. Armstrong was the team's lead rider from 1999 to 2004, according to court papers.
Charles Miller, spokesman for the Justice Department, declined to comment.
John Keker, a lawyer for Armstrong, didn't immediately respond to an e-mail message seeking comment on the lawsuit.