The Catalan giants secured a mouth-watering clash with their bitter rivals after beating Osasuna 2-1 on Thursday in the second leg of their round-of-16 clash, winning 6-1 on aggregate.
Looking ahead to the showdown against Jose Mourinho's men, Pique reckons it will be a tight affair despite Barcelona winning two out of three matches against Madrid this season.
"In a match between Barca and Madrid there are no favourites, it does not matter how they have been faring," he is quoted by AS as saying.
"We will go to the Santiago Bernabeu to try to win and get the best possible result.
"This is what the draw decided, we are going to have to prepare very well, as we always do, and try to reach the semi-finals and win the tournament."
Reflecting on the 2-1 win over Osasuna, the former Manchester United defender admitted his side struggled against their fellow La Liga side.
"It is always very hard because they close down very well, they play hard and it is always difficult to beat them.
"We had a tough time in the first half, but after the break we were superior and it is always good to come here and win."
Barcelona will travel to the Santiago Bernabeu for the first-leg of the Copa dey Rey quarter-finals on 18 January, with the return leg taking place a week later.