The Catalan giants claimed a 1-0 win when the sides met in the first leg at Camp Nou last week, with Lionel Messi netting the winner five minutes from time.
Atleti have already seen off local rivals and 2014 Copa del Rey winners Real Madrid during this season's tournament, but will need to beat Barcelona for the first time in three meetings this month if they harbour hopes of going all the way.
"Barcelona are on fire and they seem to get better with each game they play," said midfielder Tiago. "But we are not scared of Barcelona. It is great to be able to play them.
"It is a great opportunity for us against world-class players. Messi and Neymar are really good and are in great form. We can only stop them as a team."
The winner will face either Villarreal or Getafe in the semi-finals, with the former holding a 1-0 advantage from the first leg.
Like Messi for Barca, Bruno settled that encounter in the 85th minute at El Madrigal, but Villarreal will have to be on their guard as they take their narrow advantage to Coliseum Alfonso Perez on Thursday.
On the other side of the draw, Sevilla face arguably the toughest task of any of the last-eight clubs, as they look to overturn a 3-1 first-leg defeat at home to Espanyol.
Felipe Caicedo, Sergio Garcia and Lucas fired the hosts into a 3-0 lead at Estadio Cornella-El Prat last week, but Carlos Bacca's stoppage time strike gave the UEFA Europa League champions a glimmer of hope.
And Espanyol striker Christian Stuani insists his side will take nothing for granted.
"From the referee's whistle to the end of the game we will have to concentrate in Seville," he said. "We are all aware that it is vital for the club. Everyone is hoping to get through to the next round, but we are keeping our feet on the ground.
"Sevilla at their own stadium are a great team with quality players. We have to play the match with humility and intellect."
In the round's remaining tie, Athletic Bilbao and Malaga will both be aiming to end a runs of five matches without a win in all competitions.
The first leg between the sides ended goalless.
