Di Stefano passed away on Monday afternoon following a heart attack two days earlier and tributes for the 88-year-old have been flooding in since.
The Argentina-born forward was a true great during his time at the Bernabeu, scoring in five successive European Cup finals as Real Madrid won the trophy every year between 1956 and 1960. His long-standing record of 216 goals in 262 league appearances was only broken by Raul in 2009, and although Raul - as well as Andrei Shevchenko and Ruud van Nistelrooy - have now scored more European Cup goals than Di Stefano, his ratio of 49 goals in 58 matches stands alone.
By the time Di Stefano left the Bernabeu for Espanyol in 1964, he had collected eight Primera Division titles, five European Cups and a Copa del Rey winners' medal and had also been named European Footballer of the Year on two occasions.
Perez, who had visited Di Stefano at the General Universitario Gregorio Maranon Hospital in Madrid before his death, held a press conference on Monday where he paid the ultimate tribute to the club legend.
"Alfredo was the best in every sense of the word, for how he revolutionised football and for the values he had. Now it is our duty to tell those who never him saw him play that he changed everything. Madrid was his home and his life and we will give him the homage he deserves.
Tributes from the football world
Other tributes came in from the likes of FIFA president Sepp Blatter, who Tweeted: "Sad to learn of Di Stefano's passing, the most complete player I've seen. My favourite player. A legend is gone. RIP."
Pele also spoke of his sadness at the news, saying Di Stefano was responsible for breaking down barriers within the game. The Brazil great Tweeted: "Back when we played, Santos and Real Madrid were for many years primary rivals, for having the best football teams in the world.
"Today, the openness between Latin American players and European clubs is very much due to the work of Alfredo Di Stefano. He was a trailblazer, and most of all, he was a legend of the game. God rest his soul."
Former Manchester United manager Sir Alex Ferguson and club director Sir Bobby Charlton both praised Di Stefano as one of the best players of all time, while current Madrid ace Cristiano Ronaldo labelled him a "maestro".
Di Stefano's body will lie in repose in the presidential box at the club's Santiago Bernabeu stadium from Tuesday morning, at the request of the deceased, while it is likely he will be remembered ahead of the FIFA World Cup™ semi-finals taking place over the next two days.