Reinaldo Rueda's side have collected four points from their opening two games in Group A, while their opponents were thrashed 4-0 by Brazil in their only game of the tournament so far.
Colombia kicked off their Copa America campaign with a narrow win over Ecuador last Monday.
Edwin Cardona netted the only goal of the game on the stroke of half time from a well-worked free kick, and Rueda's men would hold on for the victory despite being outplayed for portions of the game.
In their second game, Colombia took on a Venezuela side with a long list of absentees through positive coronavirus tests, but they were unable to break the deadlock with the game finishing as a goalless draw.
While that was a rather disappointing result and Rueda's side are yet to hit their stride, they do find themselves on the brink of reaching the knockout stage, with four points from their opening two games.
With four sides out of five in the group reaching the next round, Colombia would gain a seven-point lead over Peru with a victory on Monday, booking their spot in the quarter-finals, while they will still aim to finish as high as possible to gain a more favourable quarter-final tie.
They take on a Peru side who will likely compete for the final two qualification spots with Ecuador and Venezuela.
Ricardo Gareca's side suffered a crushing defeat in their opening game on Friday, as they took on host nation Brazil in Rio de Janeiro.
It took just 12 minutes for the favourites to go ahead through Alex Sandro, and they kept a one-goal lead for the majority of the encounter until Neymar doubled the lead in the 70th minute, before goals from Everton Ribeiro and Richarlison in the dying minutes sealed an eye-catching 4-0 win.
Although their morale will have definitely taken a hit from that thrashing, Gareca's men have no time to dwell as they quickly return to action and have a chance to bounce back with what would be a crucial win.
With Ecuador having also lost their opening game and Venezuela sitting on just one point from their two matches, Peru still have every chance of taking one of the spots in the top four, although they may have to gain an extra point over their competitors to counteract their inferior goal difference.
They will look to go into pole position to reach the final eight with a win on Monday, before they play the two most important games against the sides they are battling for third and fourth spots with.
Colombia will come into this game without Porto winger Luis Diaz, who will serve a suspension after he was shown a red card in the dying minutes of the goalless draw with Venezuela.
His minutes have been limited, though, with Rueda preferring Juan Cuadrado and Edwin Cardona on the flanks.
Rueda opted to change the defence for the Venezuela clash, with Tottenham Hotspur centre-back Davinson Sanchez returning to the side to reform the established pairing alongside Everton's Yerry Mina at the heart of the back four.
Despite conceding four last time out, they may look to stick with the established back four of Marcos Lopez, Christian Ramos, Luis Abram and Aldo Corzo on this occasion, shielding Orlando City goalkeeper Pedro Gallese.
Colombia possible starting lineup:
Ospina; Munoz, Mina, Sanchez, Tesillo; Cuadrado, Barrios, Uribe, Cardona; Muriel, Zapata
Peru possible starting lineup:
Gallese; Corzo, Abram, Ramos, Lopez; Yotun, Tapia; Cueva, Pena, Carrillo; Lapadula
We say: Colombia 3-0 Peru
Although Colombia are yet to fully get going in the Copa America this year, Peru looked fairly poor against Brazil, and this could be the best opportunity for La Tricolor to record a convincing win to build momentum for the final eight.
With their place in the quarter-finals all but sealed, they will look to avoid dropping into the lower spots which could draw them against Argentina or Uruguay in the first knockout round, instead battling hard to ensure a top-two finish.
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