Giordano, a 50-year-old business owner from Gaithersburg, Maryland, has granted four interviews to investigators and accompanied them twice on visits to the area where he said Gardner disappeared while they went snorkeling, Lopez said in a written statement.
Giordano is scheduled to appear before a judge Monday for a detention hearing.
Aruban Solicitor General Taco Stein has said that investigators believe the 35-year-old woman from Frederick, Maryland, is dead.
Giordano, a self-employed businessman and twice-divorced father of three sons, has denied any wrongdoing since the disappearance of Ms Gardner, who authorities now believe is dead.
FBI agents combed through Giordano's Gaithersburg, Maryland, home last night.
Yesterday, solicitor general Taco Stein said a pink shirt and black sandals found during a search of an abandoned phosphate mine - near where Giordano told authorities Gardner disappeared - did not belong to the woman.
Giordano has told authorities that Ms Gardner never made it back to shore after the two became separated.
'He can't control his anger,' his first wife, Sharon Cohen, wrote in court papers in 2001.
Giordano married Cohen in 1987 and they had three sons, but the relationship deteriorated until they divorced in 2003.
Giordano apparently struggled with relationships after his first marriage ended.
The woman met with prosecutors, but told authorities she didn't want to pursue the case.
She claimed in court documents that Giordano retaliated by putting revealing photos of her in neighbours' mailboxes.
Jeanette Farago, a former neighbour, started dating Giordano around the time of his second divorce.
She said Giordano was charismatic but could become angry and possessive, though she said she never felt physically threatened.
Giordano and Ms Gardner, who is from Frederick, Maryland, arrived in Aruba on July 31 and shared a room at a Marriott hotel.
Charges would be filed at the end of the 60 days if prosecutors take the case to court.