Gonzalez said he has asked the Department of Foreign Affairs to cancel the passport of Trinidad and put him under the watchlist of the Bureau of Immigration.
The DOJ chief said he has also asked the Philippine consulate in Los Angeles to coordinate with the US Federal Bureau of Investigation for the early return of Trinidad.
He said the DOJ would prepare the extradition request to be sent to the US government.
Trinidad, a dentist, allegedly financed kidnap gangs in the country and had an P850,000 bounty on his head.
He was arrested by the FBI agents at his residence in West Covina near Los Angeles, California on Thursday.
Officials of the Department of the Interior and Local Government said Trinidad was arrested while trying to sell a van to an FBI agent who posed as buyer.
The National Anti-Kidnapping Task Force (Naktf) and the FBI had been working since March to capture Trinidad.
They got a break last month after members of the Filipino community in West Covina told them their prey was engaged in the vehicle buy-and-sell business in the area as a cover, officials said.
Trinidad did not resist arrest when five FBI agents went on Thursday to his Los Angeles home pretending to buy his van.
Philippine National Police (PNP) chief Director General Edgar Aglipay said Trinidad was this year’s biggest catch in the government’s anti-kidnapping efforts.
Several Philippine courts issued arrest warrants for Trinidad, who is the alleged mastermind of six kidnappings in 2001 alone, Aglipay said.