According to a report in The Sun newspaper doctors treating the singer in Vienna said that, despite speculation, he is not suffering from any other health issues.
They added that the 48-year-old had been in intensive care because of the 'severity and extension' of the illness.
And, The Sun added, doctors have made it clear he will need a period of 'complete rest' to recover.
In a statement, Professors Gottfried Locker and Christoph Zielinski said, 'The latest development in Mr Michael's case, which has evolved from a severe pneumococcal infection, necessitated intensive care due to its severity and extension.
'We are happy to announce that Mr Michael is improving steadily with an impressive regression of pneumonic symptoms and follows a steady rate of improvement as hoped.
'There are no other health issues with regards to the patient other than the underlying pneumonic disorder, and no further measures had to be taken.
'Mr Michael is receiving precisely the same treatment as any ordinary patient in Austria would receive at the hospital for this disease.'
The Wham! star had to axe his Symphonica tour after being taken ill in the Austrian capital last week.