Real face city rivals Atletico Madrid in Saturday's final and know they can win the trophy for a 10th time - commonly referred to as La Decima - if they can defeat the Spanish champions.
Hierro was the last Real skipper to lift the famous trophy after they beat Bayer Leverkusen 2-1 in the 2002 final.
The desire to claim a tenth title has hung over the Santiago Bernabeu ever since and Hierro hopes they can end their drought with victory in Lisbon.
"It could be that a small obsession exists now," Hierro told Marca.
"12 years have passed now without winning one, and for Real Madrid 12 years is a long time.
"But I think the true obsession existed in 1998, when we had gone 32 years without winning it.
"Generations of players and fans didn't know what it was to win the European Cup. But then we won it and it was like being freed.
"Because of this we also then won the eighth and ninth titles. Hopefully the same can happen again.
"I hope they can win La Decima and overcome this small issue."
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