The Argentine icon is backing his former side to triumph in the Champions League final against city rivals Atletico Madrid and bring home La Decima on Saturday
The local rivals clash in Lisbon, both trying to complete a double, with Atleti having already sealed La Liga glory and Real winning the Copa del Rey against Barcelona last month.
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"The support will be important. In our time there weren't big stadia like this," he is quoted as saying by Marca.
"Hopefully we'll win La Decima. The boys are going to bring home the cup.
"Madrid are a very good team, always respecting Atletico, and we want to win the European Cup playing well. The team are playing well, with a good front line and movement.
"In finals, you don't know what will happen but they are united. The team have the quality to prove themselves. But another thing is that you can be nervous if you're not lucky.
"Madrid have their category and Atletico theirs. Atletico are excited, are winning and have a good support. But I hope that Madridistas answer with an ovation for their players."
Di Stefano was part of the Real Madrid side who won five straight European Cups in the 1950s and 1960s, and is currently honorary president of the club.