Sahin has seen a fast-rising career stall during an injury-plagued year at the Bernabeu.
Sahin penned a six-year contract with Madrid in 2011 after catching the eye during Borussia Dortmund's Bundesliga title-winning campaign the previous season, but the Turkey international experienced a frustrating time in Spain.
Struck down by injuries, he played only a handful of times for Jose Mourinho's side before joining Liverpool on a season-long loan last summer.
The 24-year-old, who returned to Dortmund on loan in January after making only 12 appearances at Anfield, does not regret making the move to Madrid, though.
He told AS: "Of course I had different expectations when I went there. But I was injured. I didn't play well when I was able to return to the team and the whole time I was injured the team were really playing very well.
"Now, when I see how my game is improving, I think I took the right decision to go. I learned a lot. I was able to train day in day out with the best players in the world, like Cristiano (Ronaldo), (Karim) Benzema, (Gonzalo) Higuain...This helped me a lot to improve my game."
Dortmund will come face-to-face with Madrid later this month when they clash in the Champions League semi-finals.
Madrid have won a record nine European Cup crowns but have not tasted success in the competition since 2002 and in the last two years have been knocked out at the semi-finals.
Sahin knows what a 10th title means to Madrid and believes that increases the pressure on Mourinho's men.
He said: "Real Madrid have spent 10 years talking about and hoping to win a 10th European Cup title. 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."