The 23-year-old has been linked with a new challenge after a disappointing initial campaign in Spain, but he is eager to fight for a place in Jose Mourinho's squad
The Turkey international, who signed for Madrid last summer for an undisclosed fee, struggled for fitness and form in his first season at the Santiago Bernabeu, making just 10 official appearances for the club.
A loan spell has been suggested as a possibility for Sahin, but the former Borussia Dortmund ace has stated that he wants to prove himself with Los Blancos.
"Unfortunately, this was not a very good season for me, because of the injuries that I sustained," he told Sky Sport Italia.
"But to have success at Real Madrid is not easy at all, especially in your first year. But I am convinced that next season will be my season.
"The physical problems blocked me, and this happened for several months, including in the pre-season. But I feel just fine now and I do not have any problem.
"I hope that I will win many titles with Madrid, who are a great club. Life has given me many good things, but my dream is to win the Champions League with this club.
"If I manage to do it, I will be the luckiest man in the world."
Sahin has been a bit-part player under Jose Mourinho so far, but the Turkish midfielder had nothing but praise for the Portuguese coach.
"He is very demanding," Sahin explained. "He demands the most out of every player, but we understand this.
"On the other hand, he has no problem to praise a player when they do what he asked for."