The Bundesliga side, who famously defeated holders Inter Milan 7-3 on aggregate to reach the semi-final three seasons ago, expect to be classified as the outsiders, but they still fancy their chances of another major coup.
"It could hardly have been any harder for us, but we'll rise to the challenge and I'm looking forward to both games," said midfielder Julian Draxler.
"It's a real Champions League highlight. It was always my dream to play against Real Madrid, and to play at the Bernabeu."
That dream will come true when the Royal Blues travel to Spain for the second leg on March 18, three weeks after the first leg at the Arena AufSchalke.
The aim will be to arrive at that game with the tie still alive.
"It's going to be very difficult," admitted Kevin-Prince Boateng."But if we are united and pull in the same direction, then we always have a chance over two games.
"Real Madrid are one of the best teams in the world."
Whether Jens Keller will still be in charge of those two games remains to be seen with the Schalke coach still under pressure with his side only sixth in the Bundesliga.
However, he too hopes to be involved in what he defined a "great draw".
"To be able to measure ourselves with the most famous football club in the world with players like Cristiano Ronaldo, Iker Casillas or Gareth Bale - that's really something to look forward to," he said.