Press officer Sabine Kehm said Schumacher's family was at his side as he remained in a medically induced coma following Sunday's accident in which his head slammed into a rock while he was skiing in the French Alps, Radio France Internatioanle reported.
"At the moment, he is stable," Kehm said.
Doctors have ruled out transferring Schumacher out of the hospital in Grenoble because they said it would be "dangerous."
Besides being in a medically induced coma to spur recovery, Schumacher's body temperature was lowered to 95 degrees F to help reduce swelling, RFI said.
While circumstances surrounding the accident remain unclear, a source close to the investigation told RFI Schumacher's helmet was smashed "in two" by the impact. Schumacher had been skiing with friends and his son Mick, 14, when the accident occurred.
The 44-year-old German, who retired from the circuit for a second time in 2012, won the Formula 1 championship seven times in his racing career.