Jose Mourinho's side, reeling after falling four points behind arch rivals Barcelona in the title race, have a 3-1 advantage from last week's quarter-final, first leg at the Bernabeu and are chasing their first Cup triumph since 1993.
Success across town at the Calderon on Thursday would set up a last four clash against holders Sevilla or Villarreal, who drew 3-3 last week in Villarreal and play later on Tuesday.
Atletico's chances of a comeback have been hurt by an injury to Argentina forward Sergio Aguero.
"We know how much games against Real Madrid mean to our fans and our players," Atletico coach Quique Sanchez Flores said after his side claimed a morale-boosting 3-0 victory against Real Mallorca in La Liga on Monday to end a poor run of form.
"We have to go out and score quickly. It's about more than just getting through to the semi-finals."
Atletico have not won a Madrid derby in more than a decade and conceded a farcical third goal late in the first leg that makes their task on Thursday that much harder.
Real have progressed to the next round in all five previous domestic cup ties in which they have won the first leg 3-1.
RESPECT REQUIRED
While Real have one foot in the last four, Barcelona are virtually assured of their spot in the semi-finals.
Pep Guardiola's side, who set a club record of 28 matches unbeaten in all competitions on Sunday, thumped second-division leaders Real Betis 5-0 in the first leg, although the coach is taking nothing for granted.
"We have to prepare ourselves very well mentally," Guardiola said at a news conference after Barca's 4-1 La Liga win against Malaga on Sunday.
"I don't want any lack of respect shown to an opponent as strong as Betis. We have to take the match very seriously because there could be surprises."
Almeria have a slight advantage over Deportivo La Coruna in the other quarter-final tie after they beat the Galicians 1-0 at home last week.
If they can build on Sunday's fine home draw against Real Madrid and go through they will face Barca in the last four.
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