The 82-year-old was admitted to Sao Paulo's Albert Einstein hospital late last month to treat the infection and reassess chemotherapy.
"Still with no forecast for discharge, the patient continues to show improvement in his clinical condition, especially the respiratory infection," read a hospital statement signed by three doctors.
Pele is the only player to win the World Cup three times, lifting the trophy in 1958, 1962 and 1970.
In recent years, he has faced a series of health issues, including problems related to his spine, hip, knee and kidneys. Last year, the former Santos and New York Cosmos star underwent surgery to remove a tumor in his colon.
Pele has posted regular messages on social media in recent weeks to update fans on his health while he watches the World Cup.
"I'm strong, with a lot of hope and I follow my treatment as usual. I want to thank the entire medical and nursing team for all the care I have received," he wrote last week.
