Not only are Ferrer and Almagro seeded first and second at this event, they have won the last two Copa Claro tournaments.
Ferrer, the defending titleholder, came from behind for a 2-6, 6-4, 6-0 victory in the second round over David Nalbandian.
Nalbandian lost in the finals at Sao Paulo last week to Rafael Nadal and was the winner of this tournament five years ago.
Almagro, who fell to Ferrer in the finals of this tournament in 2012, advanced by downing Andrey Kuznetsov 7-6 (7-5), 6-2.
Other second-round contests Thursday saw No. 3 seed Stanislas Wawrinka down Daniel Gimeno-Traver 6-1, 6-4, No. 6 Fabio Fognini dismiss Marco Trungelliti 7-5, 6-2 and No. 8 Albert Ramos win over Leonardo Mayer 6-3, 7-6 (7-3).
Tommy Robredo, another former Buenos Aires champion, moved on with a 6-3, 6-1 decision over Sebastian Schwartzman. Julain Reister outlasted Aljaz Bedene 6-1, 1-6, 6-2.
Ferrer will meet Fognini in the quarterfinals while Almagro will take on Federico Delbonis.