The teams have previously been drawn against each other in the Champions League four times in the past 11 seasons, with Atletico on the losing side all four times, most notably in the 2014 and 2016 finals.
Heading into the latest chapter of their rivalry on Europe's biggest stage, Atletico are in better form than their opponents and are second in the LaLiga standings, two points ahead of Real.
"We are facing a rival that we respect. We know our strengths, we play to their full potential and we will try to take the game to a place where we can hurt them," Simeone told reporters ahead of Tuesday's meeting at the Santiago Bernabeu.
"History exists, and Madrid's history in the Champions League is extraordinary. Tomorrow we will surely have a new opportunity...
"I always put Barcelona and Madrid in the place they are in because of the history they have, but we are pure growth, which is very nice."
Simeone added that the tie was a great occasion for all involved, adding: "For the city it is spectacular, for Spain, to be able to have a Spanish team in the quarter-finals and for us who are going to play, to enjoy it."
If Atletico are to claim a win over Real, they will need 25-year-old striker Julian Alvarez to be firing on all cylinders.
The Argentine international, who scored in Atletico's 1-0 win over Athletic Bilbao on Saturday, has netted 21 times in all competitions since signing from Manchester City in August in a deal reportedly worth 75 million euros ($78.56 million).
"He is very young. He needs to continue in this way, he has to keep developing, he has room for improvement," Simeone said.
"Hopefully his teammates and the coaching staff will help him continue to grow. He looks full with energy, with the desire to do more. That will influence his growth."