The seven-times world champion is being treated at Grenoble hospital in Switzerland, near to his home, after being moved there from Lausanne in France last month. In June he emerged from a six-month coma caused by a skiing accident on 29 December 2013.
Schumacher's improving condition has revived hopes that he soon may be allowed to go home although doctors have stressed that he will need constant support. The 45-year-old is said to be answering questions from family members by moving his eyelashes.
The newspaper added that British drivers Lewis Hamilton and Jenson Button had both written letters of support to their former rival.
"You are always in my prayers," Hamilton wrote. "Prayers of hope that you will pull through this difficult time."
Meanwhile Button said: "He's fighting his greatest battle right now and I know everyone at Formula One will hope that he will win again. I certainly hope he will."
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His wife, Corinna, personally thanked fans for their support over the year at last weekend's German Grand Prix.
Writing in the official programme for the race, she said: “The German Grand Prix gives me the perfect opportunity to cordially thank you for all your good wishes and positive energies you keep sending Michael. I have to say your sympathy blew us all away! Good to know that together we made it through the hardest time!
“Now we are facing a phase which will presumably take a long time,” she added. “We trust that time will be Michael's ally in this fight. Until then I would like to wish you and your families all the best as well.”
Speaking to German women's magazine, Neue Post, Corinna was quoted as saying: "It's getting better, slowly certainly, but in any case it's improving.