The German club will confront the defending Spanish champions in the semi-finals of the competition.
"Real Madrid have spent 10 years talking about and hoping to win a 10th European Cup title," he told AS.
"In every game they play at the Bernabeu the fans end up singing about the '10th'. It shows how important it is to them and what this competition means to them.
"But this also puts them under a lot of pressure. We don't have this pressure. The tie is open. Both teams like to play attractive attacking football."
Sahin joined Dortmund on loan from Madrid in January, having left Jurgen Klopp's side to move to the Spanish outfit in the summer of 2011.