Nadal cruised past Argentina's Federico Delbonis 6-1, 6-1 at the famed Buenos Aires Lawn Tennis Club.
Next up for Nadal is Buenos Aires resident Carlos Berlocq, who handled Slovenian left-hander Blaz Rola 6-1, 6-3.
Almagro won this event in 2011 and was the runner-up in 2012. Robredo captured the Buenos Aires title back in 2009.
Meanwhile, Argentine crowd favorite Juan Monaco upended No. 3 seed Pablo Cuevas, of Uruguay, 7-6 (7-1), 6-7 (4-7), 6-4. The former top-10 star Monaco titled here in 2007 and was the '09 runner-up to Robredo.
Monaco will meet Almagro in Saturday's semifinals.
The 2015 Buenos Aires titlist will collect $91,050.