But he will have to do without Morelia striker Miguel Sabah, who did not make the initial 26-man provisional squad as he struggles to recover from a tendon injury in his leg.
Dos Santos' exclusion means Aguirre's squad contains only five recognised midfielders.
However, defender Rafael Marquez, a team-mate of Dos Santos' at the Nou Camp can play in midfield if required.
Mexico, who are preparing for the World Cup in Germany, are in Group A with hosts South Africa, Uruguay and France.
Goalkeepers: Memo Ochoa (America), Luis Ernesto Michel (Chivas), Oscar Perez (Chiapas)
Defenders: Rafael Marquez (Barcelona), Ricardo Osorio (Stuttgart), Hector Moreno (AZ Alkmmar), Francisco Rodriguez (PSV Eindhoven), Carlos Salcido (PSV Eindhoven), Paul Aguilar (Pachuca), Efrain Juarez (Pumas UNAM)
Midfielders: Jonny Magallon (Guadalajara), Jorge Torres Nilo (Atlas), Gerardo Torrado (Cruz Azul), Israel Castro (Pumas UNAM), Andres Guardado (Deportivo La Coruna)
Forwards: Pablo Barrera (Pumas UNAM), Adolfo Bautista (Guadalajara), Alberto Medina (Guadalajara), Cuauhtemoc Blanco (Veracruz), Javier Hernandez (Guadalajara), Giovani dos Santos (Galatasaray), Guillermo Franco (West Ham), Carlos Vela (Arsenal).
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