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.
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."
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.
