The sixth and final matchday will see River host San Jose on Wednesday, while Tigres travel to Juan Aurich.
River (-2) and San Jose (-5) are level on four points, two adrift of Juan Aurich (-1), who occupy the second and final qualification spot with Tigres (+8) already assured of a place in the knockout rounds.
Gallardo's River still have an opportunity to keep their Libertadores campaign alive but they must beat San Jose and hope Juan Aurich fail to win against Tigres.
A draw between Juan Aurich and Tigres and a win to River would leave the two clubs vying for second level on seven points, the tie-breaker will be determined by goal difference, followed by goals scored and away goals scored.
Juan Aurich and River have both scored five goals apiece heading into the midweek fixtures, but the Argentine champions hold the upper hand when it comes to away goals scored, having netted three compared to the former's two following the 2-2 draw at Tigres.
River's chances rest on Tigres, who have nothing to play for at Estadio Elias Aguirre, but Gallardo hopes the Mexican pace-setters treat the encounter with respect.
"Tigres is not going to play to lose. We have faith that Tigers will take a strong team to Peru," Gallardo told reporters.
"We have to win our match. By more than two goals, if it's possible.
"We got a last chance at the end and we have to believe in it."
High-flying Boca Juniors can cap a remarkable Group Five campaign with victory over Palestino on Thursday.
Boca have won all five fixtures so far, scoring 17 goals and conceding a mere two to leave Palestino and Wanderers battling out for second spot.
Palestino are level on seven points with Wanderers, who are on the road against point-less Zamora on the same day.
Cruzeiro can seal their passage into the knockout rounds at Huracan in the penultimate Group Three fixture on Tuesday.
Club Universitario - second in the table - host winless Mineros de Guayana.
In Group Eight on Tuesday, leaders Racing Club entertain Deportivo Tachira, while Sporting Cristal face Guarani.
Corinthians will be out to make it five wins from as many games when they host defending champions San Lorenzo in Group Two on Thursday.
Danubio and Sao Paulo, who are still in contention for a knockout-round berth, will meet on Wednesday.
Group Four leaders Emelec go head-to-head with The Strongest on Wednesday and Universidad Chile play second-placed Internacional, who are adrift on goal difference heading into Thursday's clash.
Meanwhile, Colo Colo and Santa Fe are scheduled to lock horns in Group One on Wednesday, with Atlas and Atletico Mineiro in action also.
