The 88-year-old was admitted to Madrid's Gregorio Maranon hospital on Saturday after being taken ill while eating in a restaurant near Real's Santiago Bernabeu home.
Di Stefano has a history of heart trouble and underwent surgery for a quadruple heart bypass, and his condition is described as "severe".
A statement released by the Spanish Football Federation read: "Alfredo Di Stefano, of 88 years of age, remains in the Coronary Unit of the Cardiology Department in the Hospital General Universitario Gregorio Maranon after suffering a cardiac arrest.
"Despite having a severe heart condition, the patient is in a stable condition."
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.
