The Andalusian club added around 60 million euros worth of players to the team led by former Real coach Manuel Pellegrini, including 20 million euros for Spain playmaker Santi Cazorla.
While Pellegrini has targeted a top-six finish in La Liga and a place in European competition next season, Malaga's owner, Sheikh Abdullah Al-Thani, will be keen for them to show in the Cup that some of the money spent is starting to bear fruit.
Jose Mourinho's Real steamrollered Malaga 4-0 in a league game at the Rosaleda in October and Cazorla is under no illusions about the scale of the task that faces them at Real's Bernabeu arena.
"They are the second-best team in the world right now, behind Barcelona, and they are proving it day-by-day," Cazorla told a news conference on Sunday.
"It's going to be a very tough game and hopefully we can get something positive out of it to keep our chances alive for the return leg," the former Villarreal player added.
"In the league, Madrid had five or six goal-scoring chances and netted four and it was game over.
"Playing at home with the fans behind them we'll have to be focused and not make any mistakes because they are expensive. If the team plays at a good level we can challenge them."
Even if Malaga can get past Real, their likely opponent in the last eight will present no less of a challenge to their bid for silverware this season.
Barca, who lost 1-0 to Real in the 2011 final, will play the winners of the Real-Malaga tie if they can dispose of La Liga rivals Osasuna, with the first leg being played at the Nou Camp on Wednesday.
NOTABLE ABSENTEES
Last month's draw also set up a clash between Valencia and Sevilla on Thursday and Real Sociedad and Real Mallorca on Wednesday in the only other all-La Liga ties.
Third-tier Albacete, who knocked out Atletico Madrid, play Athletic Bilbao on Tuesday, Mirandes, also in the third division and conquerors of Villarreal, face Racing Santander the same day and second tier Alcorcon and Cordoba play Levante and Espanyol on Tuesday and Thursday respectively.
Real could be without Angel di Maria on Tuesday after he damaged a thigh muscle in training last week.
The Argentina winger has been a key player for Mourinho's side this season, scoring four goals in La Liga and one in the Champions League and providing 12 assists.
Malaga also have a couple of notable absentees, with Brazil forward Julio Baptista and former Spain winger Joaquin both sidelined by injury.
"They'll notice Di Maria's absence a bit for sure but whoever plays it's going to be difficult," Cazorla said.
"We also have important players missing, like Baptista, who has been out for a long time, and now Joaquin, who is a key player who brings great things to the team."
The return legs
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