Di Stefano, who celebrated his 88th birthday on Friday, was said to be taken to the intensive care unit at Madrid's Gregorio Maranon hospital and is in a critical condition.
Real Madrid's honorary president is understood to have received CPR from medical emergency team Samur after suffering the heart attack on a street near Real's Bernabeu stadium.
Argentina-born forward Di Stefano represented both his native country and Spain at international level and is widely regarded as one of the finest footballers of all time.
During an 11-year spell with Real spanning from 1953 to 1964, he won eight La Liga titles, five European Cups and was named European Footballer of the Year in 1957 and 1959.
He scored 308 times in 396 competitive appearances for the European champions.
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