The 44-year-old coach says the Turk will give in a better account of himself in the Spanish capital after the winter break, having had a tough time with injury since his move
Since moving to the Spanish capital in the summer, the midfielder has made just a handful of appearances, but Klopp feels that the Turk will make his mark at Santiago Bernabeu in time.
"Everybody knows that the Spanish media exaggerates positive and negative. Nuri is an impatient guy, but nobody should forget that he was injured for a long time," Klopp told Bild.
"I am sure that he will make a better account of himself after the winter break."
However, Klopp has refused to rule out the possibility of Sahin returning to the Bundesliga to represent his old side.
"Although the issue [of a transfer back to Dortmund] is not there now, I will always have an open ear for Nuri Sahin. Of course we are in close contact," he admitted.
The 23-year-old has made three appearances for Jose Mourinho's side as he returns from a knee injury.