The 41-year-old World Cup victor was diagnosed after falling ill on Friday and was rushed to the Can Misses Hospital on the Spanish island of Ibiza.
Several hours later Ronaldo asked to be transferred to a private hospital called Clinica Nuestra Senora del Rosario, the newspaper added.
Ronaldo Nazario was admitted to hospital in Ibiza to be treated for pneumonia, with the former Brazil and Real Madrid great set to be discharged on Monday.
The newspaper's sources said the ex-footballer was still in intensive care, but was making good progress.
Brazil icon Ronaldo has offered an update on his personal wellbeing following reports he was hospitalised with flu on Friday.
Ronaldo, regarded as one of the world's best-ever players, owns a house in Ibiza and is a regular visitor to the party island, which has always been hugely popular with Brits. He is thought to have arrived on the island a few days ago before his illness started.More news: In wake of critical book, Trump calls Omarosa 'a lowlife'
He retired from football in 2011 after a glittering career with Barcelona, Inter Milan and Real Madrid. Throughout a prosperous career, he scored 62 goals in 98 global appearances for Brazil.
Ronaldo scored 62 times for Brazil, including both goals when they beat Germany in the 2002 World Cup final.
During his playing career, Ronaldo was famous for his blistering pace and phenomenal goal-scoring record.More news: Parker Solar Probe: Nasa launches mission to 'touch the Sun'
Since retirement, however, he has battled thyroid problems and gained significant weight.More news: Trump condemns racism, year after Charlottesville
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