According to the Fairfax papers, Davis underwent some procedures on the injury but is now expected to leave intensive care on Thursday.
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However he will remain in hospital for at least a week and there is still no timeframe on his expected recovery period.
"He was diagnosed with bleeding from his kidney and treating this has been the focus of doctors over the past three days. We are pleased that he has shown some very positive signs over the past 24 hours which is encouraging for everyone," chief executive David Matthews said.
"Our primary concern is obviously Phil's health and recovery. At this stage it's still hard to say how long that recovery period will be but he is progressing well and resting comfortably."