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Police received an anonymous tip that Robyn Gardner, 35, was buried in a "dog's grave," according to the paper.
Authorities have reportedly conducted a massive search in the area looking for the suspected grave.
The anonymous tipster alleges that Gardner's travel companion, Gary Giordano, beat Gardner and suffocated her, the National Enquirer reports. He then allegedly tied her arms and legs, put a bag over her head and buried her in a dog's grave, according to the report.
"He dug up a fresh dog's grave with his hands, removed the dog's body, widened the hole and put Robyn in it. He placed the dog's body on top of hers -- and covered them up," a source told the National Enquirer.
The source alleges that Gardner began moving and moaning as he filled up the grave, according to the National Enquirer.
Giordano, 50, has been behind bars since his arrest in August, three days after Gardner disappeared.
Giordano told police Gardner was swept out to sea while the two were snorkeling together.
Giordano is currently serving out a 60-day detention, which will expire Oct. 31. At that point, he'll return to court, where prosecutors will either charge him criminally or request a final detention extension for 30 more days.