Atletico have a 2-0 advantage over the holders from last week's first leg at the Calderon and knocking Real out of the competition would mark the latest triumph for the Spanish capital's second club over their neighbours.
Diego Simeone's men beat Real to win the Spanish Super Cup in August and followed up with a 2-1 success at the Bernabeu in La Liga in September.
Real then embarked on a Spanish record run of 22 straight victories before losing at Valencia in La Liga and at Atletico in the Cup.
Atletico fullback Juanfran dismissed the suggestion that the defeat at Barca would affect the way he and his team mates performed on Thursday.
The winners of the tie will almost certainly meet Barca in the quarter-finals as the record winners have a 5-0 advantage ahead of their second leg at Elche on Thursday.
"However today's match had turned out, Madrid will want to turn the tie around," Juanfran told reporters.
"We will not allow that and I am convinced that we will get through," added the Spain international.
Real, the European and world champions, bounced back from the consecutive defeats with a 3-0 La Liga victory at home to Espanyol on Saturday.
Clubs often use the Cup to give second-string players a chance to shine but coach Carlo Ancelotti is planning to field the strongest possible side.
"We have time to prepare well for the match," Ancelotti said after the Espanyol game.
"The best team will play because we will try to turn the tie around and do all we can to get to the quarter-finals," added the Italian, who led Real to Champions League and King's Cup triumphs in his first season in charge in 2013-14.
"Everyone is looking forward to this match but we have to remain calm for now. We will prepare and we will be playing at home which will help us."
This season's edition of the Cup is the first time since 1969-70, when teams from lower divisions began competing, that only top-flight sides reached the last 16.
Valencia and Sevilla are on track to meet in the quarter-finals, as are Malaga and Athletic Bilbao and Villarreal and Getafe.
(Editing by Sudipto Ganguly)
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