Sahin is on loan from Real Madrid having found it hard to break into the team under Mourinho.
The Turkey international was also linked with a move to Arsenal but suggested that he chose Liverpool because he will fit into the team more easily.
"I have a lot of self-confidence to say that I can play if the manager trusts me," said Sahin. "I'm not the kind of player who dribbles around four or five players and shoots.
"I like to control the game, to get the team on a tactically high level.
"I'm not here to be a hero. As a team we can become heroes."
Sahin also spoke of his desire to help Liverpool return to the Champions League after watching them lift the trophy in 2005 in Istanbul.
He continued: "At half-time it was 3-0 and the Liverpool fans were crying around us.
"Then Dietmar Hamann comes on and it all changes. They people think 'maybe'. Then at 3-2 it was crazy, I had goosebumps."
Sahin could feature for Liverpool against Arsenal on Sunday.