Oliveira is reportedly under pressure after Cruzeiro were eliminated by rivals Atletico Mineiro in the semi-finals of the Campeonato Mineiro on Sunday but the Brazilian coach is unfazed by the reports heading into his side's decisive sixth and final matchday fixture.
Cruzeiro welcome Bolivia's Universitario to Estadio Governador Magalhaes Pinto on Tuesday in a top-of-the-table clash, with the Brazilian hosts one point adrift of the group leaders.
Argentine side Huracan, who travel to lowly Mineros de Guayana of Venezuela on the same day, are also in the mix to advance to the knockout stages of the competition, with only two points separating first and third.
Oliveira, who has guided Cruzeiro to back-to-back Serie A titles since taking the reins in 2013, holds no fears about his job as he looks to steer the Belo Horizonte club out of the group.
"In Brazilian football, culture, falls on the coach but I am optimistic what I'm doing, putting an offensive team forward," Oliveira told reporters on Sunday.
"I am ready to receive any kind of criticism. Fear nothing.
"I am honest, loyal and do the best job. I am prepared for any situation, improve the team and to rate the team on Tuesday, with confidence and optimism."
Oliveira added: "This Cruzeiro fought, created opportunities, we had belief in the squad. There is no problem.
"It is a matter of honour to play a strong game [against Universitario], even if [Giorgian De] Arrascaeta does not play and Alisson is not among [the squad]."
Atletico Nacional, Libertad and Estudiantes also have plenty to play for in Group Seven on Tuesday.
Colombia's Nacional and Paraguayan outfit Libertad are level on points and share the same goal difference but the former tops the standings having scored a greater number of goals in five matches so far.
And the two teams go head-to-head at Estadio Atanasio Girardot Medellin.
Argentine team Estudiantes, who are one point adrift in third spot, travel to Barcelona in Ecuador.
Group One pacesetters Santa Fe and Colo Colo can secure their passages into the next round with victories on Wednesday.
Despite sharing nine points apiece, Santa Fe top the group ahead of Colo Colo on goal difference heading into respective fixtures against Atlas and Atletico Mineiro.
Atlas and Mineiro are level on six points.
In Group Two, victory against leaders and Brazilian rivals Corinthians will be enough for second-placed Sao Paulo to advance.
Defending champions San Lorenzo must beat winless Danubio if they are to stand any chance of qualifying.
Group Four high-flyers Internacional host The Strongest, who are second in the table by one point.
Emelec - three points behind Internacional - entertain Universidad Chile.
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