The 41-year-old Brazilian is said to have been diagnosed with the illness, after being rushed to Can Misses Hospital on the island.
Respected island daily, Diario de Ibiza, said he had asked for a transfer to a private hospital called Clinica Nuestra Señora del Rosario, just before midnight on Friday.
It quoted hospital sources as saying he was still in intensive care but he was making good progress.
Staff at Can Misses Hospital said they were unable to give out any information for “data protection reasons.”
Ronaldo owns a house in Ibiza and is a regular visitor to the island.