There has been a "slight improvement" in Michael Schumacher's condition, a source close to the Formula One legend said on Monday, eight days after a skiing accident left him with life-threatening injuries.

Schumacher remains in critical condition in hospital, where he has been in a medically-induced coma since the accident on Dec 29 in the French ski resort of Meribel, where he owns a chalet.

But there are small signs of improvement and his family hopes he will pull through, the source told the German sports news agency SID, on condition of anonymity.

Earlier, doctors treating Schumacher said he remained in a stable but critical condition.

"The clinical state of Michael Schumacher is considered 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's condition as critical."

The team treating Schumacher said it 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."

Meanwhile, French prosecutors said they would brief journalists this week on the investigation into Schumacher's accident.

A media conference will be held on Wednesday in 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-course 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 course to require some kind of protection or signage.

They are also examining whether the safety releases on Schumacher's skis operated properly in a probe aimed at determining responsibility for the accident.

A German news magazine reported last week that one safety release was faulty.

The investigators hope a helmet-mounted camera Schumacher was wearing will provide some clues as well as footage taken by a 35-year-old German steward who said 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 courses 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 kilometers an hour".

The witness plans to hand over the footage to French investigators.

At a media conference last week, doctors who treated Schumacher said he had been skiing at great speed when he fell.