Colombia won Group A with seven points, sending them to Cordoba for the quarter-final contest.
The South Americans are the only team not to have conceded thus far in the Copa.
In the last two competitive meetings, Colombia won one and drew the other against Peru in the Conmebol 2010 World Cup Qualifiers.
A win would take Colombia to their first semi-finals since 2004 when they lost to Argentina 3-0.
Falcao is Colombia's top scorer with two goals after bagging a brace in the 2-0 win over Bolivia to finish out their group stage matches.
The winner of the contest will play the winner of Argentina and Uruguay in the next round for a spot in the final.
Peru advanced to the quarter-finals as the top third-placed team with four points.
The Peruvians have made the quarter-finals six consecutive times in the Copa America.
Peru have not made it to the semi-finals since the 1997 tournament when they beat Argentina 2-1 in the quarter-finals before losing 7-0 to Brazil in the last four.
Paolo Guerrero has scored both of Peru's goals in the tournament so far.
PROBABLE LINE-UPS
Colombia:
Martinez; Zuniga, Yepes, Perea, Armero; Sanchez, Guarin, Aguilar, Moreno, Ramos; Falcao.
Colombia will opt for the same starting XI that earned a 2-0 victory over Bolivia in their last outing, with star striker Radamel Falcao leading the attack.
Peru:
Libman, Acasiete, Vilchez, Carmona, Rodriguez; Vargas, Cruzado, Labonton, Balbin; Guerrero, Advincula.
Juan Manuel Vargas and Paolo Guerrero are the main changes from the squad that fell 1-0 to Chile. The stars are back after receiving a breather in the final game having already qualified for the quarter-finals.
Prediction
Colombia's defence has been the best out of any team thus far in the Copa America. If they can make it four consecutive games without allowing a goal, the attack led by Radamel Falcao should be able to convert on a couple chances and secure their participation in the semi-finals.
Editor's Prediction
Colombia 2-0 Peru 
