On Thursday, doctors started to coax the German legend out of an artificial coma he was placed in after a fatal skiing accident in December.
The L'Equipe newspaper had reported that very reliable sources", said Schumacher has responded "positively" to several neurological tests since Monday.
France-based SKY News has also quoted its sources suggesting Schumacher is responding to instructions.
But recovery is not guaranteed, say doctors. "The patient may well stay in a coma," said Audibert, who is treating the champion.
The purpose of an induced coma is to allow the brain to rest so as to lower the pressure inside the skull caused by bruising and bleeding in the brain. Once the pressure had been lowered and stabilised, doctors can start lifting an induced coma, said Audibert.
"Recovery can be a very long road. In some case, patients improve between a year and three years later," the doctors said.