He said personal conflict might be the motive for the murder of Mr Schneider.
The victim, Wayne Rodney Schneider, was kidnapped by five masked men from his rented house in Bang Lamung district on November 30.
Mr Bagnato was arrested by Cambodian police but his extradition to Thailand to face the charge was not elaborated at the conference. His neck was broken.
The former member of Hells Angels had been beaten unconscious and kidnapped at gunpoint from his home in the back of a black Toyota Vigo at about 5am local time.
Blood and bullet casings, as well as paraphernalia used for taking crystal meth, were found at the scene and police have been reviewing CCTV cameras.
Malkoun, who had been drinking with Schneider and Bagnato earlier on the evening of the abduction, denied any knowledge of the kidnapping when interviewed by Thai police.
Royal Thai Police Commissioner, Police General Chakthip Chaichinda said Bagnato conspired with four others in the kidnap of Schneider and later killed him before burying the body near a cemetery at Wat Yanna Sanvararam temple in Sattahip.
Antonio Bagnato, from New South Wales, was arrested in Cambodia on Friday after Thai police named him as the ringleader of a gang of five foreigners allegedly involved in the kidnapping and murder of the 37-year-old.
Police are now hunting for the remaining three suspects - one American and two Australians. He was wanted over the shooting of a bouncer in the knee outside the Sapphire Suite nightclub in Kings Cross in 2006.
Police said the young Californian, who has lived in Pattaya since early this year, confessed he played a part in the crimes under interrogation yesterday.
Mr Schneider showed up in Thailand a month ago, paying $5,000 to rent a villa for half a year.
Malkoun, a former head of Australia's outlaw Comanchero biker gang and a convicted large-scale heroin trafficker, left Melbourne in 2013 to settle in Dubai.