WWW- TABLOID publisher American Media Inc. paid a woman who allegedly had an affair with California Gov. Arnold Schwarzenegger $20,000 to keep quiet about the relationship while wooing the movie star-turned-pol for a business deal days after he announced his run for office.

That was the bombshell claim in yesterday’s Los Angeles Times, which further reported that American Media, which owns the National Enquirer, also signed a friend of the woman to a similar confidentiality agreement about the relationship for $1,000.

American Media’s contract with actress Gigi Goyette is dated Aug. 8, 2003 – two day after Schwarzengger announced his candidacy on the Jay Leno show. Under the agreement, Goyette could not disclose to anyone besides AMI any information about her “interactions” with Schwarzenegger.

The Enquirer had published a cover story two years earlier describing an alleged seven-year affair between Goyette and Schwarzengger during his marriage to Maria Shriver. But after AMI bought out Goyette, and her friend Judy Mora, the tab never investigated further.

A former American Media employee told the L.A. Times that the company was protecting Schwarzenegger because it was negotiating a multimillion dollar deal to hire him as executive editor of Flex and Muscle & Fitness magazines in a bid to lure readers and advertisers.

“AMI systematically bought the silence” of the women, the ex-staffer said. Schwarzenegger “was a de facto employee and he was important to their bottom line.”

AMI spokesman Stu Zakim declined to comment about the L.A. Times story. Rob Stutzman, the governor’s communications director, told the Times he believed Schwarzenegger did not know of American Media’s deals with the women.

In an interview with the paper, Goyette did not dispute an account in Laurence Leamer’s new book, “Fantastic: The Life of Arnold Schwarzenegger,” that she and Schwarzenegger had a periodic intimate relationship. Leamer writes that Goyette described her contact with Schwarzenegger with the term ” ‘outercourse,’ because it’s like foreplay.” The interaction, she told him, “was whatever we wanted it to be.”

Goyette’s lawyer, Charlotte Hassett, told the Times, “She maintained it was more of a massage situation – however you want to interpret that.” Schwarzenegger spokeswoman Margita Thompson said, “I’m not going to characterize the relationship.”