The FBI and local authorities in Aruba are both investigating the policy, which names Giordano as the beneficiary, as a possible motive in 35-year-old Gardner's presumed death, ABC News reports.
"We are investigating travel insurance taken out by Gary Giordano," Aruba's Solicitor General Taco Stein tells PEOPLE. "We asked the American authorities to look into it. We do not have the ability to look into an American insurance policy from here."
Although ABC News has reported the policy is for $1.5 million, Stein says he has heard varying amounts, ranging from $500,000 to $1 million to $1.5 million. "The report by ABC is too loud, too soon," Stein says, adding investigators have yet to determine the significance of the insurance.
Gardner went missing on Aug. 2 when Giordano, 50, says they went snorkeling together but she never returned.
Stein has not wavered from his position that he believes Gardner is dead.
Asked whether insurance would be a motive for murder, he tells PEOPLE: "[It's] hard to say. If [Giordano] is on the insurance policy, if this is the first time he took out insurance and he upped the benefits, it might be interesting."
Giordano was arrested on Aug. 5 when he attempted to leave the country. Although no charges have been filed, he has been locked up since that time. He was ordered this week to remain in an Aruban jail for 16 more days as authorities look into the case further, including what they have said are inconsistencies in his story.
Reporting by Siobhan Morrissey
Courtesy Andrew Colson