The 44-year-old was said to be in a state of coma following the accident in which he hit his head.
Neurosurgeons treating him have performed a second operation on Schumacher's brain, news.com.au reports.
The hospital treating the racing legend said that Schumacher was suffering a serious brain trauma with coma on his arrival, which required an immediate neurosurgical operation.
According to the report, Schumacher had been skiing off-piste in the upmarket Meribel resort when he fell and hit his head on a rock.
The quality of recovery depends on severity of initial injury, acuteness and amplitude of pressure rise when hematoma forms, rapidity with which it is drained, and the quality of neuro intensive care and rehab.
Schumacher, who won the last of his world titles in 2004 and definitively retired in 2012 in the Brazilian Grand Prix, in which he finished seventh, is to have his 45th birthday next Friday.