McGowan has signed with Pacos Ferreira in a deal, sealed in-principle in January, while Cirio and fringe players George Mells, John Hall and Jesse Makarounas won't be offered new contracts by Adelaide.
Captain Eugene Galekovic, midfielder Marcelo Carrusca and defender Iacappo La Rocca are also weighing up their futures at the Reds, who are searching for a new coach after Guillermo Amor's resignation.
United said the new coach will decide the futures of off-contract players including South Korean midfielder Kim Jae-Sung, Eli Babalj, Marc Marino and Mark Ochieng.
Centre-back McGowan on Wednesday confirmed his move to Portugal, revealing he had declined bigger-money offers from Korea.
"I wanted to give myself a really good chance of making the Socceroos and show that ambition that's required to be in the national team," McGowan told Fox Sports.
"Hopefully, this move can put me in the window for that and then I can play well enough to get that chance."