It was announced earlier this afternoon that former striker Di Stefano had passed away at the age of 88 in the Spanish capital after suffering a heart attack over the weekend.
"It was with immense sadness I learned of the death of Alfredo Di Stefano, a wonderful man I had the fortune to know during my time in Madrid," Mourinho told the Blues' website.
"Of course I first send my thoughts to his family and friends, but also this is a very sad day for football and football fans, which we all are, when we lose a special person like this.
"Alfredo was the best Real Madrid player in history - winning five consecutive European Cups - and one of the greatest of all time. Rest in peace Alfredo."
Widely regarded as one of the all-time best footballers, Di Stefano scored in all five European Cup victories as Madrid dominated the continent in the mid-to-late 1950s.