The 41-year-old Brazilian was rushed to Can Misses Hospital on Friday after being diagnosed with the illness.
Later that night, the Brazilian requested a transfer to the Nuestra Señora del Rosario hospital, owned by private health company Policlinica.
Former Brazil star Ronaldo was admitted to hospital in Ibiza last Friday with a case of pneumonia.More news: Tiger Woods live, TV schedule, coverage Sunday
The newspaper's sources said the ex-footballer was still in intensive care, but was making good progress.
Contacted by AFP, a hospital spokeswoman said she was unable to give any information for privacy reasons.
No-one at the private hospital Ronaldo is now said to be a patient at could be contacted early on Sunday for comment.More news: Paul Pogba named Manchester United captain against Leicester
Ronaldo, regarded as one of the world's best-ever players, owns a house in Ibiza and is a regular visitor to the island. Tissue swells, and it can cause coughing and breathing difficulties. Throughout a prosperous career, he scored 62 goals in 98 global appearances for Brazil.
He won his first cap for Brazil as a 17-year-old and went on to score 62 goals in 97 worldwide appearances, including both goals when Brazil beat Germany 2-0 in the 2002 World Cup final.
The former Real Madrid forward, who also played for Barcelona, Inter Milan and AC Milan, thanked his fans for their love and well wishes.More news: Maryland coach DJ Durkin placed on leave by administration as investigation begins
He finished his career with 12 goals in the World Cup finals, tying with Pele for the all-time record.