He is part of a 39-man squad named by manager Eduardo Berizzo and was one of 20 players to take part in a training session on Monday.
Balbuena, who has eight caps, will also hope to make the final cut when Berizzo selects his final 23-man squad for the tournament, which kicks-off in Brazil on 14 June.
Should he do so he will be involved in a warm-up fixture with Honduras in his home city of Ciudad del Este on Wednesday 5 June.
Balbuena would be West Ham’s sole representative at the Copa America, should he make Berizzo’s final squad.
Manuel Lanzini and Carlos Sanchez have not been included in preliminary squads named by Argentina and Colombia respecitvely but Felipe Anderson has been left out of Brazil’s 23-man selection.