Staff at both hospitals refused to give an update on the 41-year-old's health for privacy reasons when contacted by Diario de Ibiza. "Thank you all for the messages and affection!"
The former Real Madrid and Barcelona forward was said to have been rushed to intensive care in Ibiza after being struck down with pneumonia, eventually being transferred to a private hospital, Clinica Nuestra Señora del Rosario.
It quoted hospital sources as stating that Ronaldo was still in intensive care but that he was making good progress.
Ronaldo, who retired in 2011 had a glittering football career with top European clubs including Barcelona, Real Madrid and Inter Milan.
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It also tied the 36-hole record for all majors, matching Jordan Spieth at the 2015 Masters, Martin Kaymer at the 2014 U.S. Open at Pinehurst No. 2 and Brandt Snedeker (Royal Lytham & St.
No-one at the private hospital Ronaldo is now said to be a patient at could be contacted early on Sunday for comment.
The Brazilian, regarded as one of the world's best-ever players, owns a house in Ibiza and is a regular visitor to the island. Two of those were the only ones that Brazil scored against Germany in the 2002 World Cup final.
Retired Brazilian striker Ronaldo said Sunday he is in hospital with a "bad flu" on the Spanish holiday island of Ibiza but reassured fans that he will be out in a day.
He picked up the Ballon d'Or award for the best player in the world in 1997 and 2002.