Unnamed people familiar with the investigation told the Journal the allegations stem from his 2008 presidential campaign, and include a claim that the married Richardson, now 64, arranged for supporters to pay $250,000 to a woman who had planned to say they engaged in an affair.
The report said the woman supposedly planned to sue the former governor, but the nature of the suit was unknown.
The grand jury is sitting in Albuquerque. Prosecutors are seeking to portray any payment as a campaign contribution.
The Journal said several of Richardson's associates have been granted immunity in exchange for their testimony before the grand jury, one of several to examine Richardson's administration and campaigns in recent years.
The newspaper said Richardson was attending an environmental conference in Nigeria this week and didn't return calls or e-mails for comment. His office also declined to provide the names of his lawyers, the Journal said.
The U.S. attorney's office in Albuquerque also refused to confirm or deny the grand jury investigation.
At least one Richardson associate, Jennifer Poersch, the senior finance adviser for his campaign, told the Journal she was "not aware of any wrongdoing or inappropriate fundraising." She also said she had not been called to testify before the grand jury.
The alleged investigation was first reported by the Albuquerque Journal two weeks ago.
If genuine, the investigation comes after former North Carolina Sen. John Edwards, who also sought the Democratic nomination for president, has been indicted over allegations he conspired to solicit money from political backers to support his mistress and a former aide to keep an extramarital affair hidden during the 2008 campaign. Edwards pleaded not guilty but faces trial in January.
Notable deaths of 2014 [PHOTOS]