Last week there were reports that the racing driver, who struck his head on a rock in the Alpine resort of Meribel, had been experiencing moments of consciousness.
The reports came after doctors had warned Schumacher may never recover and could be left in a permanent vegetative state.
The 45-year-old had been put in an induced coma to reduce brain swelling at a French hospital following the accident on December 29. He has also undergone surgery to remove lesions from his brain.
His former track rival Jean Alesi said on Thursday he had noticed significant improvements recently. He said: "During my last visit I noticed something had improved. I felt a relief among his family, a great happiness at how things were developing. That is brilliant - even if the road back is still a long one."
His manager Sabine Kehm said: "We are on his side during his long and difficult fight, together with the team of the hospital in Grenoble and we keep remaining confident."
His wife Corinna has reportedly been constructing a £10 million medical suite in their Swiss mansion, so her husband can be cared for at home.