Michael Schumacher remains in a critical condition in hospital where he has been in a medically induced coma since the accident on December 29 in the French ski resort of Meribel, where he owns a chalet.
But there are small signs of improvement and his loved-ones hope that he will pull through, the source told the German sports news agency SID, an AFP subsidiary, yesterday on condition of anonymity.
Earlier, doctors treating Michael Schumacher said he remained in a stable but critical condition.
"The clinical state of Michael Schumacher is considered as stable and is being constantly monitored as he receives medical treatment," a statement from Grenoble's University Hospital said.
"However, the medical team in charge of his care underlines that they continue to consider Michael Schumacher's condition as critical."
The team treating Schumacher said they would be giving no details of the treatment the 45-year-old is receiving in order to protect his right to privacy.
"The privacy of the patient demands that we are not going into details of his treatment, and this is why we do not envisage any press conferences or statements in the near future."
French prosecutors meanwhile said they would this week brief journalists on their investigation into Michael Schumacher's accident.
A press conference will be held on Wednesday at 11:00 am (1000 GMT) in the Alpine town of Albertville, local prosecutor Patrick Quincy said.
Investigators are focusing on the retired racer's speed when he fell and slammed his head on a rock on a small off-piste section, prompting his evacuation by helicopter to Grenoble.
Prosecutors are also looking at whether the limits of the ski runs next to the accident site were correctly marked and whether the rock in question was lying close enough to the piste to require some kind of protection or signage.
They are also examining whether the safety releases on Michael Schumacher's skis operated properly in a probe aimed at determining responsibility for the accident.
The investigators are hoping that a helmet-mounted camera Schumacher was wearing will provide some clues, as will footage by a 35-year-old German steward who says he was filming his girlfriend on the slopes when by chance he captured the moment when the retired driver fell.
In the background, a skier is seen descending an unmarked run between two groomed pistes before falling, the German news magazine Der Spiegel reported.
According to the witness, who spoke to the magazine, the seven-time world champion was descending the slope at a "leisurely" pace -- "a maximum speed of 20 kilometres an hour". He plans to hand over the footage to French investigators.
This would corroborate claims by Michael Schumacher's spokeswoman Sabine Kehm, who has said he could not have been going fast "because it appears he helped a friend who had just fallen".
But in a press conference last week, doctors who treated Schumacher said he had been skiing at great speed when he fell.
Michael Schumacher won more Formula One titles than any other driver and enjoyed 91 Grand Prix victories between 1994 and 2004.